## Questions on Mensuration for SSC CGL Set 86 with answers

Mensuration for SSC CGL: Solve 10 surface area and volume measurement questions in Set 86 in 15 minutes. Verify your solutions from the answers.

Answers and link to the quick solutions are at the end.

### 10 Questions on Mensuration for SSC CGL Set 86 - Answering time 15 mins

**Problem 1.**

One of the four angles of a rhombus is $60^0$. If the length of each side of the rhombus is 8 cm, then the length of the longer diagonal is,

- $\displaystyle\frac{8}{\sqrt{3}}$ cm
- $8\sqrt{3}$ cm
- $8$ cm
- $4\sqrt{3}$ cm

**Problem 2.**

Three spherical balls of radii, 2 cm, 4 cm, and 6 cm are melted to form a new spherical ball. In this process, there is a loss of 25% of the material. What is the radius (in cm) of the new ball?

- 6
- 12
- 8
- 16

**Problem 3.**

The curved surface area of a hemisphere is 27.72 sq cm, and volume is 19.404 cubic cm. Find its radius.

- 0.7 cm
- 4.2 cm
- 2.1 cm
- 1.05 cm

**Problem 4.**

The radius of cross-section of a solid right circular cylindrical rod is 3.2 dm. The rod is melted and 44 equal solid cubes of side 8 cm are formed. The length of the rod is, (take $\pi=\frac{22}{7}$)

- 56 cm
- 7 cm
- 0.7 cm
- 5.6 cm

**Problem 5.**

A prism with a right triangular base is 25 cm high. If the shorter sides of the triangle are in the ratio 1 : 2 and volume of the prism is 100 cubic cm, what is the length of the longest side of the triangle?

- $2\sqrt{5}$ cm
- $\sqrt{5}$ cm
- $5$ cm
- $5\sqrt{2}$ cm

**Problem 6.**

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

- 2.25 m
- 4.25 m
- 1.75 m
- 1.125 m

**Problem 7.**

Let ABCDEF be a prism whose base is a right-angled triangle where sides adjacent to $90^0$ are 9 cm and 12 cm. If the cost of painting the prism is Rs. 151.20 at the rate of 20 paise per sq cm, then the height of the prism is,

- 17 cm
- 18 cm
- 16 cm
- 15 cm

**Problem 8.**

In the given figure, $\triangle ABC$ is drawn such that AB is tangent to a circle at point A. The radius of the circle is 10 cm and BC passes through the center of the circle. Point C lies on the circle. If $BC=36$ cm and $AB=24$ cm, then what is the area of $\triangle ABC$ (in sq cm)?

- 148
- 166.15
- 180
- 168

**Problem 9.**

Two smaller circles touch a larger circle internally and pass through the center $O$ of the larger circle. If the diameter of the larger circle is 28 cm, what is the area of the larger circle which is not enclosed by the smaller circles?

- 256 sq cm
- 308 sq cm
- 154 sq cm
- 616 sq cm

** Problem 10.**

In the given figure, PB is one-third of AB and BQ is one-third of BC. If the area of BPDQ is 20 sq cm, then what is the area (in sq cm) of ABCD?

- 60
- 30
- 40
- 45

Know how to visualize the 2D and 3D shapes for surface area and volume calculations from the paired solution set at,

**Solutions to Mensuration for SSC CGL Set 86.**

### Answers to the questions on mensuration for SSC CGL Set 86

**Problem 1.** **Answer:** Option b: $8\sqrt{3}$ cm.

**Problem 2. Answer:** Option a : 6 cm.

**Problem 3. Answer:** Option c: 2.1 cm.

**Problem 4. Answer:** Option b: 7 cm.

**Problem 5. Answer:** Option a: $2\sqrt{5}$ cm.

**Problem 6. Answer:** Option d : 1.125 m.

**Problem 7. Answer:** Option b: 18 cm.

**Problem 8. Answer:** Option b: 166.15.

**Problem 9. Answer:** Option b: 308 sq cm.

**Problem 10. Answer:** Option a: 60.

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