## 87th SSC CGL level Question Set, 7th on topic Mensuration

This is the 87th question set of 10 practice problem exercise for SSC CGL exam and 7th on topic Mensuration. Students should complete this question set in prescribed time first and then only refer to the corresponding solution set.

This *10 problem question* set can effectively be used as a *mini-mock test on SSC CGL Mensuration*.

*After taking the test,* you may refer to the detailed solutions at * SSC CGL level Solution Set 87, Mensuration 7*, for step by step explanation of the solutions accompanied by suitable figures. In any case, the

*answers to the questions are given at the end.*

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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### 87th question set - 10 problems for SSC CGL exam: topic Mensuration 7 - Answering time 15 mins

**Problem 1.**

In the figure below O is the center of the circle and $\angle AOB=150^0$. If the shaded portion is $x$ part of the circular region, then value of $x$ is,

- $\displaystyle\frac{1}{12}$
- $\displaystyle\frac{1}{9}$
- $\displaystyle\frac{1}{4}$
- $\displaystyle\frac{1}{6}$

**Problem 2.**

If $D$, $E$, and $F$ are the mid-points of the sides of an equilateral $\triangle ABC$, then the ratio of the area of the $\triangle DEF$ and $\triangle DCF$ is,

- $1.1:1$
- $1:1$
- $1:1.1$
- $0.9:1$

**Problem 3.**

The centroid of a $\triangle ABC$ is $G$. If the area of the $\triangle ABC=72$ sq units, the area of $\triangle BGC$ is,

- 36 sq units
- 48 sq units
- 16 sq units
- 24 sq units

**Problem 4.**

In a trapezium $ABCD$, $AD || BC$, $AD \lt BC$, $BC = 6$ cm and distance between parallel sides is 4 cm. If the area of $ABCD$ is 16 sq cm, then length of $AD$ is,

- 2 cm
- 3 cm
- 1 cm
- 8 cm

**Problem 5.**

Two identical circles intersect so that their centers and points at which they intersect form a square of side 2 cm. What is the area (in sq cm) of the portion that is common to the two circles?

- $3\pi-4$
- $\pi-2$
- $4\pi-8$
- $2\pi-4$

**Problem 6.**

A solid right circular cylinder and a solid hemisphere stand on equal bases and have the same height. The ratio of their whole surface area is,

- 3 : 2
- 2 : 3
- 4 : 3
- 3 : 4

**Problem 7.**

Three medians AD, BE and CF of $\triangle ABC$ intersect at G. The area of $\triangle ABC$ is 36 sq cm. Then the area of $\triangle CGE$ is,

- 12 sq cm
- 6 sq cm
- 18 sq cm
- 9 sq cm

**Problem 8.**

The surface area of one cone is twice that of the second cone and the slant height of the latter is twice that of former. The ratio of their radii is,

- 1 : 4
- 4 : 3
- 3 : 4
- 4 : 1

**Problem 9.**

The diameter of a sphere is twice the diameter of another sphere. The curved surface area of the first and the volume of the second are numerically equal. The numerical value of the radius of the first sphere is,

- 8
- 24
- 16
- 3

** Problem 10.**

A rectangular paper sheet of dimensions 22 cm x 12 cm is folded in the form of a cylinder along its length. What will be the volume enclosed by the cylinder? (Take $\pi=\frac{22}{7}$)

- $624\text{ cm}^3$
- $400\text{ cm}^3$
- $462\text{ cm}^3$
- $460\text{ cm}^3$

### Answers to the questions

**Problem 1. Answer:** Option d: $\displaystyle\frac{1}{6}$.

**Problem 2. Answer:** Option b : 1 : 1.

**Problem 3. Answer:** Option d: 24 sq units.

**Problem 4. Answer:** Option a: 2 cm.

**Problem 5. Answer:** Option d: $2\pi-4$.

**Problem 6. Answer:** Option c : 4 : 3.

**Problem 7. Answer:** Option b: 6 sq cm.

**Problem 8. Answer:** Option d: 4 : 1.

**Problem 9. Answer:** Option b: 24.

**Problem 10. Answer:** c: $462\text{ cm}^3$.

### Other related question set and solution set on SSC CGL mensuration

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