## 42nd SSC CGL level Question Set, 4th on topic Mensuration

This is the 42nd question set of 10 practice problem exercise for SSC CGL exam and 4th on topic Mensuration. Students should complete this question set in prescribed time first and then only refer to the corresponding solution set.

We will repeat here the method of taking a 10 problem test if you have not gone through it already.

### Method for taking this 10 problem test and get the best results from the test set:

**Before start,**go through the tutorials**Basic concepts on Geometry 1**,**, Basic concepts on Geometry 2**or any other short but good material to refresh your concepts if you so require.**Basic concepts on Geometry 3****Answer the questions**in an undisturbed environment with no interruption, full concentration and alarm set at 15 minutes.**When the time limit of 15 minutes is over,**mark up to which you have answered,**but go on to complete the set.****At the end,**refer to the answers at the end of this question set to mark your score at 15 minutes. For every correct answer add 1 and for every incorrect answer deduct 0.25 (or whatever is the scoring pattern in the coming test). Write your score on top of the answer sheet with date and time.**Identify and analyze**the problems that**you couldn't do**to learn how to solve those problems.**Identify and analyze**the problems that**you solved incorrectly**. Identify the reasons behind the errors. If it is because of**your shortcoming in topic knowledge**improve it by referring to**only that part of concept**from the best source you get hold of. You might google it. If it is because of**your method of answering,**analyze and improve those aspects specifically.**Identify and analyze**the**problems that posed difficulties for you and delayed you**. Analyze and learn how to solve the problems using basic concepts and relevant problem solving strategies and techniques.**Give a gap**before you take a 10 problem practice test again.

Important:bothandpractice testsmust be timed, analyzed, improving actions taken and then repeated. With intelligent method, it is possible to reach highest excellence level in performance.mock tests

**Resources that should be useful for you**

**You may refer to:**

* 7 steps for sure success in SSC CGL tier 1 and tier 2 competitive tests* or

*to access all the valuable student resources that we have created specifically for SSC CGL, but*

**section on SSC CGL****generally for any hard MCQ test.**

**Tutorials that you should refer to**

*Basic concepts on Geometry 1 lines points and triangles*

*Basic concepts on Geometry 2 quadrilaterals polygons squares*

*Basic and rich concepts on Geometry 3 Circles*

*Basic and rich Geometry concepts part 4 Arc angle subtending concept proof*

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### 42nd question set - 10 problems for SSC CGL exam: topic Mensuration - 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

### Answers to the questions

**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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