## Mensuration questions with answers SSC CGL Set 42

Solve 10 Mensuration questions pyramid questions in SSC CGL Set 42 in 15 minutes. Verify from answers. Learn to solve quickly from solutions.

The questions are on volumes of a cuboid, right circular cones, a sphere, a cube, a sphere; areas of a right prism with square base, a pyramid and circular wheel, triangles circles. Each question is of a different type.

Answers and link to solutions are at the end.

### Mensuration questions pyramid questions for SSC CGL Set 42 - Answering time 15 mins

**Problem 1.**

A wooden box measures 20cm by 12cm by 10cm. Thickness of the wood is 1cm. Volume of the wood to make the box (in cm$^3$) is,

- 519
- 2400
- 960
- 1120

**Problem 2.**

If a right circular cone is separated into solids of volumes $V_1$, $V_2$ and $V_3$ by two planes parallel to the base, which also trisect the altitude then $V_1 : V_2 : V_3$ is,

- 1 : 7 : 19
- 1 : 2 : 3
- 1 : 4 : 6
- 1 : 6 : 9

**Problem 3.**

The largest sphere that can be carved out of a cube of side 7cm has a volume (in cm$^3$),

- 481.34
- 179.67
- 543.72
- 718.66

**Problem 4.**

The height of a right prism with a square base is 15cm. If the total surface area of the prism is 608 sq cm its volume (in cm$^3$) is,

- 910
- 920
- 980
- 960

**Problem 5.**

The base of a right pyramid is an equilateral triangle of side $10\sqrt{3}$ cm. If the total surface area of the pyramid is $270\sqrt{3}$ sq cm, its height is,

- $10\sqrt{3}$ cm
- $12$ cm
- $10$ cm
- $12\sqrt{3}$ cm

**Problem 6.**

If a metallic cone of base radius 30cm and height 45cm is melted and recast into metallic spheres of radius 5cm find the maximum number of spheres that can be made,

- 81
- 41
- 40
- 80

**Problem 7.**

The diameter of a circular wheel is 7m. How many revolutions will it make in travelling 22km?

- 1000
- 100
- 400
- 500

**Problem 8.**

In an equilateral $\triangle ABC$ of side 10cm, the side BC is trisected at D. The length of AD then (in cm) is,

- $3\sqrt{7}$
- $\displaystyle\frac{7\sqrt{10}}{3}$
- $\displaystyle\frac{10\sqrt{7}}{3}$
- $7\sqrt{3}$

**Problem 9.**

The length of perpendiculars drawn from any point in the interior of an equilateral triangle to the respective sides are $p_1$, $p_2$ and $p_3$. The length of each side of the triangle is then,

- $\displaystyle\frac{2}{\sqrt{3}}(p_1 +p_2 +p_3)$
- $\displaystyle\frac{4}{\sqrt{3}}(p_1 +p_2 +p_3)$
- $\displaystyle\frac{1}{3}(p_1 +p_2 +p_3)$
- $\displaystyle\frac{1}{\sqrt{3}}(p_1 +p_2 +p_3)$

** Problem 10.**

If arcs of same length in two circles subtend angles $60^0$ and $75^0$ at their centre, the ratio of their radii is,

- 3 : 4
- 3 : 5
- 4 : 5
- 5 : 4

Know how to visualize the 3D and 2D shapes and apply the required formulas quickly from the paired solution set at,

**Solution to mensuration questions for SSC CGL Set 42.**

### Answers to the Mensuration questions pyramid questions SSC CGL Set 42

**Problem 1.** Answer: Option a: 519.

**Problem 2.** Answer: Option a: 1 : 7 : 19.

**Problem 3.** Answer: Option b: 179.67.

**Problem 4.** Answer: Option d: 960.

**Problem 5.** Answer: Option b: $12$ cm.

**Problem 6.** Answer: Option a : 81.

**Problem 7.** Answer: Option a**: **1000.

**Problem 8.** Answer: Option c: $\displaystyle\frac{10\sqrt{7}}{3}$.

**Problem 9.** Answer: Option a: $\displaystyle\frac{2}{\sqrt{3}}(p_1+p_2+p_3)$.

**Problem 10.** Answer: Oprtion d: 5: 4.

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