# SSC Geometry questions

## SSC 2023 Geometry questions

#### Question 1

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?

#### Question 2

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:

## SSC 2022 Geometry questions

#### Question 1

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.

#### Question 2

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?

#### Question 3

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 $$\angle CBD$$?

#### Question 4

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:

#### Question 5

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?

#### Question 6

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

## SSC 2021 Geometry questions

#### Question 1

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:

#### Question 2

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:

#### Question 3

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:

#### Question 4

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:

#### Question 5

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:

#### Question 6

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

#### Question 7

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

#### Question 8

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

#### Question 9

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?

#### Question 10

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:

#### Question 11

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

#### Question 12

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