SSC Geometry questions

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:

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: