SSC Geometry Questions

A pyramid has an equilateral triangle as its base, of which each side is 8 cm. Its slant edge is 24 cm. The whole surface area of the pyramid (in $$cm^{2}$$) is:

A circle touches all four sides of a quadrilateral ABCD. If AB = 18 cm, BC = 21 cm and AD = 15 cm, then length CD is:

What is the volume of a cylinder if the radius of the cylinder is 10 cm and height is 20 cm? (Take $$\pi = 3.14$$)

The total surface area of a square-based right pyramid is 1536 $$m^{2}$$, of which 37.5% is the area of the base of the pyramid. What is the volume (in $$m^{3}$$) of this pyramid?

If the diameter of a sphere is reduced to its half, then the volume would be:

If the volume of a sphere is 38808 $$cm^{3}$$, then its surface area is:

In a circle of radius 42 cm, an arc subtends an angle of 60° at the centre. Find the length of the arc.

(Take $$ \pi = \cfrac{22}{7}$$)

The area of a rhombus having one side measuring 17 cm and one diagonal measuring 16 cm is:

The radius of a circle is 1.75 cm. What is the circumference of the circle?

(Take $$ \pi = \frac{22}{7}$$)

The radius of the base of a right circular cone is 5 cm. Its slant height is 13 cm.
What is its volume (in $$cm^{3}$$ , rounded off to 1 decimal place)? (Take $$ \pi = \frac{22}{7}$$)

A conical shape vessel has a radius of 21 cm and has a slant height of 25 cm. If the curved part of the vessel is to be painted white, find the cost (in ₹) of painting at the rate of ₹1.5 per $$cm^{2}$$.

In a $$\triangle PQR$$ and $$\triangle ABC, \angle P = \angle A$$ and $$AC = PR$$. Which of the following conditions is true
for triangle PQR and ABC to be congruent?

The total surface area of a solid hemisphere is 4158 $$cm^{2}$$. Find its volume (in $$cm^{3}$$).

Let C be a circle with centre O and radius 5 cm. Let PQ be a tangent to the circle and A be the point of tangency. Let B be a point on PQ such that the length of AB is 12 cm. If the line joining O and B intersects the circle at R, find the length of BR (in cm).

What is the volume of the largest sphere that can be carved out of a wooden cube of sides 21 cm?
(Take $$ \pi = \frac{22}{7}$$)

What will be the difference between the total surface area and the curved surface area of a hemisphere having 4 cm diameter?

The area of an equilateral triangle is $$4\sqrt{3}  cm^{2}$$. Find the side (in cm) of the triangle.

Find the area of a triangle whose length of two sides are 4 cm and 5 cm and the angle between them is $$45^{\circ}$$.

The cost of painting the total surface area of a 30 m high solid right circular cylinder at the rate of ₹25 per $$m^{2}$$ is ₹18,425. What is the volume (in $$m^{3}$$) of this cylinder [use $$ \pi \frac{22}{7}$$]?

What is the length (in cm) of the transverse common tangent between two circles with radii 6 cm and 4 cm, given that the distance between their centres is 14 cm?

The areas of the two triangles are in the ratio 4 : 3 and their heights are in the ratio 6 : 5. Find the ratio of their bases.

The volume of a sphere is given by 130977 $$cm^{3}$$. Its surface area (in $$cm^{2}$$) is:

ABCD is a cyclic quadrilateral and BC is a diameter of the related circle on which A and D also lie. $$\angle BCA = 19^{\circ}$$ and $$\angle CAD = 32^{\circ}$$. What is the measure of $$\angle ACD$$?

Find the number of diagonals of a regular polygon, sum of whose interior angles is $$2700^{\circ}$$.

PQR is an equilateral triangle inscribed in a circle. S is any point on the arc QR. Measure of $$\frac{1}{2} < PSQ$$ is:

If the height of a cone is 7 cm and the diameter of the circular base is 12 cm, then its volume is (nearest to integer):

The area of a rectangular field is 480 $$m^{2}$$. If the length is 20% more than the breadth, then the length of the rectangular field is:

In a circle centred at O, PQ is a tangent at P. Furthermore, AB is the chord of the circle and is extended to Q. If PQ = 12 cm and QB = 8 cm, then the length of AB is equal to:

The curved surface area of a cone whose base radius is 7 cm and slant height is 10 cm is:

A sector of a circle has a central angle of $$45^{\circ}$$ and an arc length of 22 cm.
Find the radius of the. circle. [Use $$\pi = \frac{22}{7}$$]

Find the area of a rhombus if the perimeter of the rhombus is 52 cm, and one of its diagonals is 10 cm long.

The diameter of a hemisphere is equal to the diagonal of a rectangle of length 4 cm and breadth 3 cm. Find the total surface area (in $$cm^{2}$$ ) of the hemisphere.

A cylindrical metallic rod of diameter 2 cm and length 45 cm is melted and converted into wire of uniform thickness and length 5 m. The diameter of the wire is:

Find the total surface area of a sphere whose volume is $$\cfrac{256}{3} \pi cm^{3}$$.

If the base radius and the height of a right circular cone are increased by 10%, then the percentage increase in the volume is:

If one of the interior angles of a regular polygon is $$\frac{15}{16}$$ times of one of the interior angles of a regular decagon, then find the number of diagonals of the polygon.

Some medicine in liquid form is prepared in a hemispherical container of diameter 36 cm. When the container is full of medicine, the medicine is transferred to small cylindrical bottles of diameter 6 cm and height 6 cm. How many bottles are required to empty the container?

The volume of a right circular cone having a base diameter of 14 cm is 196π $$cm^{3}$$. Find the perpendicular height of this cone

A cylinder has some water in it at a height of 16 cm. If a sphere of radius 9 cm is put into it, then find the rise in the height of the water if the radius of the cylinder is 12 cm.

If perimeter of the circle is 13.2 cm, then the radius of the circle is ____________.

(Take $$ \pi = \cfrac{22}{7}$$)

If the radius of two circles be 6 cm and 9 cm and the length of the transverse common tangent be 20 cm, then find the distance between the two centres.

The area of an equilateral triangle is 173.2 $$cm^{2}$$. Its side will be __________.

The perimeter of a sector of a circle is 24 cm and the radius is 3 cm. Calculate the area (in $$cm^{2}$$) of the sector.

In two circles centred at O and O’, the distance between the centres of both circles is 17 cm. The points of contact of a direct common tangent between the circles are P and Q. If the radii of both circles are 7 cm and 15 cm, respectively, then the length of PQ is equal to:

In a triangle LMN, OP is a line segment drawn parallel to the side MN. OP intersects the sides LM and LN at O and P, respectively. If LM = 15 cm, OM = 4 cm, and PN = 5 cm, then what is the length (in cm) of the side LN?

The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 90 cm. Find its area (in $$cm^{2}$$).

In a $$\triangle ABC$$, the bisectors of angle ABC and angle ACB intersect each other at point O. If the angle BOC is $$125^{\circ}$$, then the angle BAC is equal to:

In a $$\triangle PQR, \angle P : \angle Q : \angle R = 3 ∶ 4 ∶ 8$$. The shortest side and the longest side of the triangle, respectively, are:

Two circles of radius 13 cm and 15 cm intersect each other at points A and B. If the length of the common chord is 12 cm, then what is the distance between their centres?

In a triangle ABC, if $$\angle B = 90^{\circ}, \angle C = 45^{\circ}$$ and AC = 4 cm, then the value of BC is:

A right square pyramid having lateral surface area is 624 $$cm^{2}$$ . If the length of the diagonal of the square is $$24\sqrt{2}$$, then the volume of the pyramid is:

The area of a sector of a circle of radius 8 cm, formed by an arc of length 4.6 cm, is ___________.

For a triangle ABC, D and E are two points on AB and AC such that $$AD = \frac{1}{6} AB, AE = \frac{1}{6} AC$$. If BC = 22 cm, then DE is __________. (Consider up to two decimals)

The radii of the ends of a frustum of a solid right-circular cone 45 cm high are 28 cm and 7 cm. If this frustum is melted and reconstructed into a solid right circular cylinder whose radius of base and height are in the ratio 3 : 5, find the curved surface area (in $$cm^{2}$$) of this cylinder. [Use $$\pi = \frac{22}{7}$$]

The sides of a rectangle are in the ratio of 3 : 8 and its area is 1944 $$cm^{2}$$. What is its perimeter?

A solid sphere made of wax of radius 12 cm is melted and cast into solid hemispheres of radius 4 cm each. Find the number of such solid hemispheres.

In a $$\triangle PQR, \angle P=90^{\circ}, \angle R=47^{\circ}$$ and $$PS \perp QR$$. Find the value of $$\angle QPS$$.

Let ABC, PQR be two congruent triangles such that $$\angle A = \angle P = 90^{\circ}$$. If BC = 17 cm, PR = 8 cm, find AB (in cm).

$$PQR$$ is a triangle. The bisectors of the internal angle $$\angle Q$$ and external angle $$\angle R$$ intersect at $$S$$. If $$\angle QSR = 40^{\circ}$$, then $$\angle P$$ is:

The curved surface area (CSA) and the total surface area (TSA) of a hemisphere whose radius is 7 cm are:

If the hypotenuse of a right-angled triangle is 29 cm and the sum of the other two sides is 41 cm, then the difference between the other two sides is:

The height and the radius of the base of a right circular cone are in the ratio of 12 : 5. If
its volume is 314 $$cm^{3}$$, then what is the slant height of the cone? (Use $$\pi = 3.14$$)

If the radius of a sphere is doubled, then its surface area will be increased by:

AB is a chord of a circle having radius 1.7 cm. If the distance of this chord AB from the centre of the circle is 0.8 cm, then what is the length (in cm) of the chord AB?

E, F, G, and H are four points lying on the circumference of a circle to make a cyclic quadrilateral. If $$\angle FGH = 57^{\circ}$$, then what will be the measure of the $$\angle HEF$$?

If the radius of a hemispherical balloon increases from 4 cm to 7 cm as air is pumped into it, find the ratio of the surface area of the new balloon to its original.

The heights of two cones are in the ratio 7.: 5 and their diameters are in the ratio 10:21. What is the ratio of their volumes? ($$Where $$ \pi = \frac{22}{7}$$)

If radius of a sphere is decreased by 48%, then by what percent does its surface area decrease?

The difference between the length of two parallel sides of a trapezium is 12 cm. The perpendicular distance between these two parallel sides is 60 cm. If the area of the trapezium is 1380 $$cm^{2}$$, then find the length of each of the parallel sides (in cm).

In a circle, chords AB and CD intersect internally at E. If CD = 18 cm, DE = 5 cm, AE = 13 cm, then the length of BE is:

What is the area of a triangle whose sides are of lengths 12 cm, 13 cm and 5 cm?

If the external angle of a regular polygon is 18°, then the number of diagonals in this polygon is:

PQRS is a cyclic quadrilateral. If $$\angle P$$ is three times of $$\angle R$$ and $$\angle S$$ is four times of $$\angle Q$$, then the sum of $$\angle S + \angle R$$ will be:

The centroid of an equilateral triangle PQR is L. If PQ = 6 cm, the length of PL is:

In $$\triangle PQR,PQ=QR$$ and O is an interior point of $$\triangle PQR$$ such that $$\angle OPR= \angle ORP$$.
Consider the following statements:
(i) $$\triangle POR$$ is an isosceles triangle.
(ii) O is the centroid of $$\triangle PQR$$.
(iii) $$\triangle PQO$$ is congruent to $$\triangle RQO$$.
Which of the above statements are correct?

A hemispherical bowl of internal radius 18 cm is full of liquid. This liquid is to be filled in cylindrical bottles each of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?

It is given that $$\triangle ABC \cong \triangle PQR, AB = 5 cm, \angle B = 40^{\circ}$$, and $$\angle A = 80^{\circ}$$. Which of the
following options is true?

A rectangular park is 120 m long and 104 m wide. A 1-m wide path runs along the boundary of the park, remaining completely inside the park area. Thus, the outside edges of the path run along the boundary wall of the park. The inside edges of the path are marked with a white line of negligible thickness. If it costs ₹2.50 to mark each metre with the white line, then how much would it cost (in ₹) to fully mark the inside edges of the path?

What is the total surface area of a pyramid whose base is a square with side 8 cm and height of the pyramid is 3 cm?

The breadth ‘b’ of a room is twice its height and half of its length. Find the length of the longest diagonal of the room.

If the areas of two similar triangles are in the ratio 196 : 625, what would be the ratio of the corresponding sides?

What is the perimeter of a square inscribed in a circle of radius 5 cm?

If the surface area of a sphere is 30,184 $$cm^{2}$$ , then find its volume (Use $$\pi = \frac{22}{7}$$)

A,B, C are three points such that AB = 9 cm, BC = 11 cm and AC = 20 cm. The number of circles passing through points A,B,C is:

If the curved surface area of a cylinder is $$126 \pi  cm^{2}$$ and its height is 14 cm, what is the volume of the cylinder?

The length, breadth and the height of a cuboid are 24 cm, 18 cm and 12 cm respectively. It is melted to make smaller cubes. If the length of the side of the cube is 6 cm, then what is the number of cubes formed?

A solid metallic sphere of radius 21 cm is melted and moulded into small right circular cones, each of radius 7 cm and height of 3 cm. The number of such cones is:

In a trapezium ABCD, AB and DC are parallel to each other with a perpendicular distance of8 m between them. Also, (AD) = (BC) = 10 m, and (AB) = 15 m &amp;lt; (DC).
What is the perimeter (in m) of the trapezium ABCD?

AB = 28 cm and CD = 22 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 4 cm. The radius of the circle is ______ (Consider up to two decimals)

The perimeter of an isosceles triangle is 100 cm. If the base is 36 cm, then find its semi perimeter (in centimetres).

A prism and a pyramid have the same base and the same height. Find the ratio of the volumes of the prism and the pyramid.

A hemispherical bowl has a radius of 7 cm. It is to be painted from inside as well as outside. Find the cost of painting it at the rate of Rs.40 per 20 $$cm^{2}$$ ? (Take thickness of the bowl as negligible).

The sides of two similar triangles are in the ratio 5:7. The areas of these triangles are in the ratio:

Points A and B are on a circle with centre O. PA and PB are tangents to the circle from an external point P. If PA and PB are inclined to each other at $$42^{\circ}$$, then find the measure of $$\angle$$ OAB.

The diagonal of a rectangle is 12 cm long, and it is twice as long as one of the sides of the rectangle. What is the area of this rectangle?

AB is the diameter of a circle with centre O. C and D are two points on the circumference of the circle on either side of AB. such that $$\angle CAB= 42^{\circ}$$ and $$\angle ABD = 57^{\circ}$$. What is difference (in degrees) between the measures of $$\angle CAD$$ and $$\angle CBD$$?

A circle is inscribed in a ΔABC having sides AB = 16 cm, BC = 20 cm and AC = 24 cm, and side AB, BC and AC touches circle at D, E and F, respectively. The measure of AD is:

The tops of two poles of heights 18 m and 30.5 meters connected by a wire. If the wire makes an angle of $$30^{\circ}$$ with the horizontal, what is the length (in m) of the wire?

The inner circumference of a circular path enclosed between two concentric circles is 264 m. The uniform width of the circular path is 3 m. What is the area (in $$m^{2}$$, to the nearest whole number) of the path? (Taken $$\pi = \frac{22}{7}$$)

The internal length, breadth and height of a cuboidal room are 12 m, 8 m and 10 m,respectively. The total cost (in ₹) of white washing only all four walls of the room at the cost of ₹25 per $$m^{2}$$ is:

The base ofa triangle is equal to the perimeter of a square whose diagonalis $$6 \sqrt{2}$$ cm,and its height is equalto the side
of a square whose areais 144 $$cm^{2} $$. Thearea ofthe triangle (in $$cm^{2} $$) is:

The area of a square and rectangle are equal. The length of the rectangle is greater than the length of a side of the square
by 10 cm and the breadth is less than 5 cm. The perimeter(in cm)of the rectangleis:

A circle is inscribed in a triangle ABC. It touches side AB, BC and AC at points R, P and Q, respectively. If AQ = 2.6 cm, PC = 2.7 cm and BR = 3 cm, then the perimeter (in cm)of the triangle $$\triangle ABC$$ is:

Chord AB of a circle is produced to a point P, and C is a point on the circle such that PC is a tangent to the circle. If PC = 12 cm, and BP = 10 cm, then the length of AB (in cm)is:

The radius of the base of a cylinder is 14 cm andits volumeis 6160 $$cm^3$$, The curved surface area (in $$cm^2$$) is:

(Take $$\pi = \frac{22}{7}$$)

If the volumeof a sphere is 4851 $$cm^{3}$$ then its surface area (in $$cm^{2}$$) is: (Take $$\pi = \frac{22}{7}$$)

In $$\triangle ABC, \angle A = 68^\circ$$. If is the incentre of the triangle , then measure of $$\angle BIC$$ is:

In a circle with centre O, AD is a diameter and AC is a chord. Point B is on AC such that OB = 7 cm and $$\angle OBA = 60^\circ$$. If $$\angle DOC = 60^\circ$$, then what is the length of BC?

In a $$\triangle ABC$$, the bisector of $$\angle B$$ and $$\angle C$$ meet at O in the triangle. If $$\angle BOC = 134^\circ$$, then the measure of $$\angle A$$ is:

Theratio of the total surface area and volumeof a sphereis 2 : 7. Its radiusis:

In $$\triangle ABC, \angle A = 54^\circ$$. If I is the incenter of the triangle, then the measure of $$\angle BIC$$ is:

The internal measures of a cuboidal room are with length as 12 m, breadth as 8 m and height as 10 m. The total cost (in ₹) of white washing all four walls of the room and also the ceiling of the room,if the cost of whitewashing is ₹25 per $$m^{2}$$ is :

Let A and B be twocylinders such that the capacity ofA is the same as the capacity of B. Theratio of the diameters ofA and B is 1 : 4. Whatis the ratio of the heights ofA and B?

$$PQRS$$ is a cyclic quadrilateral. If $$\angle P$$ is 4 times $$\angle R $$, and $$\angle S $$ is 3 times $$\angle Q$$, then the average of $$\angle Q$$ and $$\angle R $$ is:

The sides of a triangle are 24 cm, 26 cm and 10 cm.At each of its vertex, circles of radius 4.2 cm are drawn. What is the area (in $$cm^$$) of the portion covered by the three sectors of the circle ? $$(\pi = \frac{22}{7})$$

If each side of a square is decreased by 17%, then by what percentage does its area decrease?

The sides PQ and PR of $$\triangle PQR $$ are produced to points S and T, respectively. The bisectors of $$\angle SQR$$ and $$\angle TRQ$$ meetat U. If $$\angle QUR = 59\circ$$, then the measure of $$\angle P$$ is:

One side of a rhombus is 13 cm and one of its diagonals is 24 cm. What is the area (in $$cm^2$$) of rhombus?

Thebaseof triangle is equal to the perimeter of a square whosediagonal is 9 $$\sqrt{2}$$ cm,andits height is equalto the side of a square whosearea is 144 $$cm^{2}$$. Thearea ofthe triangle (in $$cm^{2}$$) is:

A ladder is resting against a wall, The angle between the foot of the ladder and the wall is $$45^\circ$$ and the foot of the ladder is 6.6 m away from the wall. The length of the ladder(in m)is:

PA and PB are two tangents from a point P outside the circle with centre O. If A and are points on the circle such that $$\angle APB = 142^\circ$$, then $$\angle OAB$$ is equal to:

The perimeter of a square is half the perimeter of a rectangle. The perimeter of the square is 40 m. If its breadth is two- thirds of its length, then what is the area (in $$m^2$$) of the rectangle?

The perimeterof a right triangle is 60 cm and its hypotenuse is 26 cm. Whatis the area (in $$cm^{2}$$)ofthe triangle?

In $$\triangle ABC, D$$ is the median from $$A$$ to $$BC, AB = 6  cm, AC = 8  cm$$ and $$BC = 10  cm$$ .The length of median $$AD$$(in cm)is

Two circles of radii 15 cm and 10 cm intersect each other and the length of their common chord is 16 cm. What is the distance (in cm) between their centres?

A 64 cm wide path is made arounda circular garden having a diameter of 10 metres. The area (in m?)ofthe path is closest to:
$$(take \pi= \frac{22}{7})$$

In $$\triangle ABC, BD \perp AC$$ at D. E is a point on BC such that $$\angle BEA = x^\circ$$. If $$\angle EAC = 62^\circ$$ and $$\angle EBD = 60^\circ$$,then the value of $$x$$ is:

A solid metallic cylinder with a base radius of 3 cm and a height 120 of cm is melted and recast into a sphere of radius r cm. What is the value of r if there is a 10% metal loss in the conversion?

AB is a chord of a circle with centre O and P is any point on the circle. If $$\angle APB = 122^\circ$$, then what is the measure of $$\angle OAB$$?

If the radius of a circle is increased by 23%, then by what percentage will its area increase?

If the radius of a sphere is increased by $$16\frac{2}{3}\%$$, then by what per cent would its surface area increase (correct to one decimal place)

In circle with centre O and radius 13 cm, a chord AB is drawn. Tangentsat A and B intersect at P such that $$\angle APB = 60^\circ$$. If Distance of AB from the centre O is 5 cm, then what is the length (in cm) of AP?

In $$\triangle ABC, D$$ and E are the points on sides AB and AC, respectively and $$DE \parallel BC$$. BC = 8 cm and DE = 5 cm. If the area of $$\triangle ADE = 45 cm^2$$, then what is the area (in cm$$^2$$) of $$\triangle ABC$$?

Points P, Q, R, S and lie in this order on a circle with centre O. If chord TS is parallel to diameter PR and $$\angle RQT = 58^\circ$$ then find the measure (in degrees) of $$\angle RTS$$.

The base of a triangle is increased by 30%. By what percentage (correct to two decimal places) can its height be increased so that the area increases by 50%?

The radius of a cylinder is reduced to 50% of its actual radius. If its volume remains the same as before, then its height becomes k times the original height. The value of k is:

$$\triangle ABC$$ is an equilateral triangle with side 18 cm. D is a point on BC such that $$BD = \frac{1}{3}BC$$ Then length(in cm) of AD is:

A circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 8.4 cm, BC = 9.8 cm and CD = 5.6 cm. The length of side AD, in cm, is:

A rectangular plot is 420 m long and 84 m wide. lt is surrounded by semi-circular flower beds along all its sides. The area of the entire plot (in hectares) is $$x$$. The value of $$x$$ (correct to one decimal place) is (Taken $$\pi=\frac{22}{7}$$):

A $$\triangle ABC$$ has sides 5 cm, 6 cm and 7 cm. AB extended touches a circle at P and AC extended touches the same circle at Q. Find the length (in cm) of AQ.

A wooden piece in the shape of a cuboid is divided into five equal parts by cutting it with four cuts perpendicular to its length,and it turns out that each picece is a cube of volume 27 $$cm^{3}$$. That is the total surface area (in $$cm^{2}$$) of the cuboid?

ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If $$\angle BEC = 138^\circ$$ and $$\angle ECD = 35^\circ$$, then what is the measure of $$\angle BAC$$?

If each side of a rectangle is increased by 12%, then by what percentage will its area increase?

If the diameter of the base of a cone is 24 cm and its curved surface area is $$1395\frac{3}{7}$$ $$cm^{2}$$, then its height is:
(Take $$\pi=\frac{22}{7}$$)

If the length of a rectangle is increased by 80%, what would be the percentage decrease (correct to one place of decimal) in the width to maintain the same area?

In $$\triangle ABC, AB$$ and AC produced to points D and E respectively. If the bisectors of angle CBD and angle BCE meet at point O, such that $$\angle BOC = 63^\circ$$, then $$\angle A = ?$$

In $$\triangle ABC, \angle A= 90^\circ, AD \perp BC$$ at D. If AB = 12 cm and AC = 16 cm, then what is the length(in cm) of BD?

In $$\triangle ABC, DE \parallel AB$$, where D and E are the points on sides AC and BC, respectively. If AD = x-3, AC = 2x, BE = x-2 and BC = 2x + 3, then what is the value of x?

In triangle PQR, points E and F are on sides PQ and PR respectively such that EF is parallel to QR. If PE = 2 cm and EQ = 3 cm, then area($$\triangle$$ PQR) : area($$\triangle$$ PEF) is equal to:

Let $$\triangle ABC \sim \triangle PQR$$ and $$\frac{ar(\triangle ABC)}{ar(\triangle QPR)} = \frac{144}{49}$$. If AB = 12 cm, BC = 7 cm and AC = 9 cm, then PR(in cm) is equal to:

Tangent is drawn from a point P to a circle, which meets the circle at T such that PT = 8 cm. A secant PAB intersects the circle in points A and B. If PA= 5 cm, what is the length (in cm) of the chord AB?

The capacity of a cuboidal tank is 12288 kilolitres. Its length is 32 m, and its breadth and height are in the ratio of 3: 2. What is the breadth (in m) of the tank?

The lengih (in m, correct to one decimal place) of the longest pole that can be fitted in a room of dimensions 12  m $$\times$$ 6 m $$\times$$ 4  m  is:

The length and breadth of a rectangle are increased by 25% and 32%, respectively. The percentage increase in the area of the resulting rectangle will be:

The total surface area of a solid right circular cylinder of height 13cm, is 880 $$cm^{2}$$. Its volume (in $$cm^{2}$$) is 11k. The value of k is: (Taken $$\pi=\frac{22}{7}$$)

In a circle, chords AB and CD intersect internally, at E. If CD = 16 cm, DE = 6 cm, AE = 12 cm, and BE = X cm then the value of x is:

In a circle with centre O, AD is a diameter and AC is a chord. Point B is on AC such that OB = 7 cm and $$\angle OBA = 60^\circ$$. If $$\angle DOC = 60^\circ$$, then what is the length of BC (in cm)?

In a $$\triangle ABC, \angle BAC=90^{0},AD$$ is drawn perpendicular from A on BC. Which among the following is the mean proportional between BD and BC?

In $$\triangle ABC, AD$$ is the bisector of $$\angle A$$ meeting BC at D. If AC = 21 cm, BC = 11 cm and the length of BD is 3 cm less than DC, then the length(in cm) of side AB is:

Ina trapezium PQRS, PQ is parallel to RS and diagonals PR and QS intersect at O. If PQ= 4 cm. SR = 10 cm, then what is area($$\triangle POQ$$) : area($$\triangle SOR$$) ?

Point P lies outside a circle with centre O. Tangents PA and PB are drawn to meetthe circle at A and respectively. If $$\angle APB = 80^\circ$$, then $$\angle OAB$$ is equal to:

Points A and B are on a circle with centre O. PAM and PBN are tangentsto the circle at A and B respectively from a point P outside the circle. Point Q is on the major arc AB such that $$\angle QAM = 58^\circ$$ and $$\angle QBN = 50^\circ$$, then find the measure (in degrees) of $$\angle APB$$.

Points P and Q are on the sides AB and BC respectively of a triangle ABC, right angled at B. If AQ = 11 cm, PC = 8 cm, and AC = 13 cm, then find the length (in cm) of PQ.

The area of a parallelogram ABCD is $$300 cm^{2}$$, The distance between AB and CD is 20cm, and the distance between BC and AD is 30cm. What is the perimeter (in cm) of the parallelogram ?

The length and breadth of a rectangle are 35 cm and 11 cm, respectively. What will be the circumference of the circle that inscribes this rectangle? (Take $$\pi=\frac{22}{7}$$)

A rectangular room has an area of 60 $$m^{2}$$ and a perimeter of 34 m. The length of the diagonal of the rectangular room is same as the side of a square. The perimeter of the square (in m) is:

In $$\triangle ABC, AD \perp BC$$ at D and AE is the bisector of $$\angle A$$. If $$\angle B = 62^\circ$$ and $$\angle C = 36^\circ$$, then what is the measure of $$\angle DAE ?$$

Ina triangle ABC,a point D lies on AB and points E andF lie on BC suchthat DF is parallel to AC and DE is parallel to AF. If BE = 4 cm, EF = 6cm, then find the length (in cm) of BC.

Points A and B are on a circle with centre O. Point C is on the major are AB. If $$\angle OAC = 35^\circ$$ and $$\angle OBC = 45^\circ$$, then what is the measure (in degrees) of the angle subtended by the minor are AB at the centre?

The area of a triangular plot having sides 12 m, 35 m and 37 m is equal to the area of a rectangular field whose sides are in the ratio 7 : 3. The perimeter (in m) of the field is:

The area of the curved surface of a right circular cylinder is 19.5 $$m^{2}$$ and its volume is 39 $$m^{3}$$.  What is the radius (in m) of its base?

The radius of a solid lead sphere is 2 cm. 2541 such spheres are melted and recast into a cube of edge $$x$$ cm. The value of $$x$$ is (take $$\pi=\frac{22}{7}$$):

A solid metallic sphere of radius 8.4cm is melted and recast into a cone of height 18.9cm. What is the radius (in cm) of the base of the cone ?

In a circle with centre O, points A, B, C and D in this order are concyclic such that BD is a diameter of the circle. If $$\angle$$BAC = 22$$^\circ$$, then find the measure (in degrees) of $$\angle$$COD.

In triangle ABC, D is a point on BC such that BD : DC =3 : 4. E is a point on AD such that AE : ED = 2 : 3. Find the ratio area $$(\triangle ECD)$$ : area $$(\triangle AEB)$$.

Let $$\triangle$$ABC $$\sim$$ $$\triangle$$RPQ and $$\frac{ar(\triangle \text{ABC})}{ar(\triangle \text{PQR})}=\frac{16}{25}$$. If PQ = 4 cm, QR = 6 cm and PR = 7 cm, then AC (in cm) is equal to:

The are of square is S, and that of the aquare formed by joining the mid-points of the given square is A. The value of $$\frac{A}{S}$$ is equal to:

The area of a circular path enclosed by two concentric circles is 3080 m$$^2$$. If the difference between the radius of the outer edge and that of inner edge of the circular path is 10 m, what is the sum (in m) of the two radii? (Take $$\pi = \frac{22}{7}$$)

The area of the four walls of a room is 1152 $$m^{2}$$ and its length is $$\frac{5}{3}$$ times its breadth. If the height of the room is 12 m,then the area of its floor is:

The internal and external diameters of a hollow hemispherical bowl are 18 cm and 22 cm, respectively. The total surface area (in $$cm^{2}$$) of the bowl is:

The radii of the circular ends of a frustum of a cone are 20 cm and 13 cm and its height is 12 cm. What is the capacity (in litres) of the frustum (correct to one decimal place)? (Take $$\pi=\frac{22}{7}$$)

The sides of a triangular field are 96 m, 110 m and 146 m. The cost of levelling the field at ₹5.60 per $$m^{2}$$ is:

Two circles of radius 15 cm and 37 cm intersect each other at the points A and B. If the length of common chord is 24 cm, what is the distance (in cm) between the centres of the circles?

A cylindrical vessel of base radius 10.5 cm and height 30 cm is $$\frac{4}{5}$$ full of water. The entire water is poured into a rectangular tub of length 44 cm and breadth 36 cm. The height (in cm) to which the water level rises in the tub is:
(Take $$\pi = \frac{22}{7}$$) (Assuming no overflow of water)

A wire is in the form of a square of side 33 cm. If the wire is molded to form a circle, then what is the radius of the circle?
(Use $$\pi=\frac{22}{7}$$)

Angle between the internal bisectors of two angles $$\angle B$$ and $$\angle C$$ of a $$\triangle ABC$$, is $$132^\circ$$, then the value of $$\angle A$$ is:

In $$\triangle ABC$$ and $$\triangle DEF$$ we have $$\frac{AB}{DF} = \frac{BC}{DE} = \frac{AC}{EF}$$, then which of the following is true?

The area of a circular park is 12474 m$$^2$$ . There is 3.5 m wide path around the park. What is the area (in m$$^2$$) of the path?(Take $$\pi = \frac{22}{7}$$)

The diameter of an iron ball used for shot-put is 21 cm. It is melted and then a cylinder of height 3.5 cm is made. The curved surface area of the cylinder will be:
(Take $$\pi=\frac{22}{7}$$)

The perimeter of rectangular field is 386 m and the difference between its two adjacent sides is 95 m. The side of a square field, having the same area as that of the rectangle, is:

$$\triangle ABC \sim \triangle PQR$$. The areas of $$\triangle ABC$$ and $$\triangle PQR$$ are 64 cm$$^2$$ and 81 cm$$^2$$, respectively and AD and PT are the medians of $$\triangle ABC$$ and $$\triangle PQR$$, respectively. If PT = 10.8 cm, then AD =?

What is the volume(in cm$$^3$$a) ofa spherical shell whose inner and outerradii are respectively 2 cm and 3 cm ?

A chord 21 cm long is drawn in a circle of diameter 25 cm. The perpendicular distance of the chord from the centre is:

A radius of a circular park is 23 m. It has inside all around it, a 4 m wide path. Find the cost of paving the path at the rate ₹500/ $$m^{2}$$.
(Take $$\pi=\frac{22}{7}$$)

A solid cube of side 15 cm is dropped into a rectangular container of length 25 cm, breadth 20 cm and height 18 cm, which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:

Chord AB of circle of radius 10 cm is at a distance 8 cm from the centre O. If tangents drawn at A and B intersect at P, then the length of the tangent AP (in cm) is:

From a wooden cubical block of side 10 cm, a sphere of radius 4.2 cm is carved out. How much wood is wasted in the process?
(Use $$\pi=\frac{22}{7}$$)

From each of the four corners of a rectangular sheet of dimensions 48 cm x 27 cm, a square of side 3.5 cm is cut off and a box is made. The volume of the box is:

In a circle with centre O, AB is a chord of length 10 cm. Tangents at points A and B intersect outside the circle at P. If OP = 2 OA, then find the length (in cm) of AP.

In $$\triangle ABC, AB = 20$$ cm, BC = 21 cm and AC = 29 cm. What is the value of $$\cot C + \cosec C - 2 \tan A$$?

In $$\triangle$$ABC, $$\angle$$C = 90$$^\circ$$ and Q is the midpoint of BC. If AB = 10 cm and AC = $$2\sqrt{10}$$ cm, then the length of AQ is:

The total surface are of a hemisphere is very nearly equal to that of an equilateral triangle. The side of the triangle is how many times (approximately) of the radius of the hemisphere?

Four solid cubes, each of volume 1728 $$cm^{3}$$, are kept in two rows having two cubes in each row. They form a rectangular solid with square base. The total surface area (in $$cm^{2}$$) of the resulting solid is:

If the internal dimensions of a rectangular closed wooden box are 30 cm, 18 cm and 23 cm, what space (in $$cm^{2}$$) will it occupy, if the wood used is 1 cm thick?

In a triangle ABC, point D lies on AB, and points E and F lie on BC suchthat DF is parallel to AC and DE is parallel to AF. If BE = 4 cm, CF = 3 cm, then find the length (in cm) of EF.

In triangle ABC, P and Q are the mid points of AB and AC, respectively. R is a point on PQ such that PR : RQ = 3 : 5 and QR = 20 cm, then what is the length (in cm) of BC?

Points A, D, C, B and E are concyclic. If $$\angle$$AEC = 50$$^\circ$$ and $$\angle$$ABD = 30$$^\circ$$, then what is the measure(in degrees) of  $$\angle$$CBD?

The area of a triangular field with sides 60 m, 175 m and 185 m is equal to that of a rectangular park whose sides are in the ratio of 21 : 10. The perimeter (in m) of the park is:

The sum of the length, breadth and height of a cuboid is 28 cm. lf the total surface area of the cuboid is 558 $$cm^{2}$$ then its diagonal is:

There is a rectangular plot, 120m long and 98m wide, with semi-circular flower beds along the breath on both sides of the plot. The cost of putting a fence all around the plot at ₹16.50 per m is: (Taken $$\pi=\frac{22}{7}$$)

Two circles of radii 10 cm and 12 cm intersect each other and the length of their common chord is 16 cm. What is the distance (in cm) between their centres?

The area of a trapezium, whose parallel sides are 25 cm and 19 cm long, is 330 $$cm^{2}$$. The distance between the sides (in cm) is:

The material of a sphere of radius r is melted and recast into a hollow cylindrical sell of thickness a and outer radius b. What is its length asssuming that no material is lost in recasting?

Two similar cylindrical jugs have heights 5 cm and 8 cm, respectively. If the capacity of the smaller jug is 64 $$cm^{3}$$, what is the capacity ( correct to 2 decimal places, in $$cm^{3}$$) of the larger jug?

What is the length (in cm) of the smallest altitude of the triangle whose sides are 5 cm, 12 cm and 13 cm? (correct to one decimal place)

ABCD is a cyclic quadrilateral such that when sides AB and DC are produced, they meet at E, and sides AD and BC meet at F, when produced. If $$\angle$$ADE = 80$$^\circ$$ and $$\angle$$AED = 50$$^\circ$$, then what is the measure of $$\angle$$AFB?

If one of the angles of a triangle is $$74^\circ$$, then the angle between the bisectors of the other two interior angles is:

In a right angled triangle ABC, the lengths ofthe sides containing the right angle are 5 cm and 12 cm respectively. A circle is inscribed in the triangle ABC. Whatis the radius ofthe circle (in cm)?

In $$\triangle ABC, D$$ and are the points on sides AB and AC,respectively such that $$\angle ADE = \angle B$$. If AD = 7 cm, BD = 5 cm and BC = 9 cm, then DE (in cm) is equal to:

The area of the floor of a cubical room is 147 $$m^{2}$$. The length of the longest rod that can be kept in the room is:

The base of a triangle is 8.5 cm and height is 14 cm. The height of another triangle, having base 14 cm and double the area of the first triangle, is:

The bisector of $$\angle A$$ in $$\triangle ABC$$ meets side BC at D. If AB = 12 cm, AC = 15 cm and BC = 18 cm, then the length of DC is:

The lengths of one side and a diagonal of a rectangle are 63 cm and 65 cm, respectively. What is the perimeter (in cm) of a square whose area is one-seventh of that of the rectangle?

Triangle ABC is right angled at B and D is a point of BC such that BD = 5 cm, AD = 13 cm and AC = 37 cm. then find the length of DC in cm.

$$\triangle$$ABC $$\sim$$ $$\triangle$$DEF and the area of $$\triangle$$ABC is 13.5 cm$$^2$$ and the area of $$\triangle$$DEF is 24 cm$$^2$$ . If BC = 3.15 cm, then the length (in cm) of EF is:

If the area of the base of a cylinder is $$346.5 cm^{2}$$ and the area of the curved smface is $$990 cm^{2}$$, then its height is: (Taken $$\pi=\frac{22}{7}$$)

If the height of a cylinder is increased by 30%, and the radius of its base is decreased by 15% then by what percentage will its curved surface area change?

If the side of a square is increased by 40%, then its area will be increased by:

Ina circle with centre O, PAX and PBY are the tangents to the circle at points A and B, from an external point P. Q is any point on the circle such that $$\angle QAX = 59^\circ$$ and $$\angle QBY = 72^\circ$$. What is the measure of $$\angle AQB$$?

The perimeter of a circular lawn is 1232 m. There is 7 m wide path around the lawn. The area (in m$$^2$$) of the path is:(Take $$\pi = \frac{22}{7}$$)

The volume of a wall whose height is 10 times its width and whose length is 8 times its height is 51.2 m$$^3$$ . What is the cost(in ₹) of painting the wall on one side at the rate of ₹100/ m$$^2$$ ?

If the radius of a cylinder is decreased by 40% and the height is increased by 60% to form a new cylinder, then the volume will be decreased by:

In triangle ABC, D and E are the mid points ofAB and BCrespectively. If area($$\triangle CED$$) = 8 cm$$^2$$, then what is the area(ADEC) in cm$$^2$$ ?

In $$\triangle$$ABC, $$\angle$$A = 50$$^\circ$$. If the bisectors of the angle B and angle C, meet at a point O, then $$\angle$$BOC is equal to:

Kamala has three cylindrical containers, each with radius 20 cm that she wants to fill with grain. If her bag of grain contains 100 kg grain, and she fills all three containers to a height of 70 cm, how much grain will be left in the bag, if 1 kg grain occupies 3000 $$cm^{2}$$ space? (Use $$\pi=\frac{22}{7}$$)

The area of a table top in the shape of an equilateral triangle is $$9\sqrt{3}$$ cm$$^2$$. What is the length (in cm) of each side of the table?

The cost of tiling the floor of a rectangular room is ₹9100 at ₹65 per m$$^2$$ . Theratio of the length and breadth of the floor is 7 : 5. The perimeter (in m ) of the floor of the room is:

The radius of a cylinder is increased by 20% and its height is decreased by 45%. What is the percentage increase/decrease in the volume of the cylinder?

The ratio of the curved surface area and total surface area of a cylinder is 4 : 7. If its volume is 4851 $$cm^{3}$$ , then its radius is:
(Take $$\pi=\frac{22}{7}$$)

Triangles ABC and DBCareright angled triangles with common hypotenuse BC. BD and ACintersect at P when produced. If PA= 8 cm, PC = 4 cm and PD = 3.2 cm, then the length of BD,in cm, is:

A path 6 m wide runs around and outside of a rectangular plot of length 10 m and breadth 8 m. The area (in $$cm^{2}$$) of the path is: