## 86th SSC CGL level Question Set, 6th on topic Mensuration

This is the 86th question set of 10 practice problem exercise for SSC CGL exam and 6th 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 86, Mensuration 6*, 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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### 86th question set - 10 problems for SSC CGL exam: topic Mensuration 6 - 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

**Answers** to the questions follow.

### Answers to the questions

**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.

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

**SSC CGL level Solution Set 88 on Mensuration 8**

**SSC CGL level Question Set 88 on Mensuration 8**

**SSC CGL level Solution Set 87 on Mensuration 7**

**SSC CGL level Question Set 87 on Mensuration 7**

**SSC CGL level Solution Set 86 on Mensuration 6**

**SSC CGL level Question Set 86 on Mensuration 6**

**SSC CGL level Solution Set 43 on Mensuration 5**

**SSC CGL level Question Set 43 on Mensuration 5**

**SSC CGL level Solution Set 42 on Mensuration 4**

**SSC CGL level Question Set 42 on Mensuration 4**

**SSC CGL level Solution Set 41 on Mensuration 3**

**SSC CGL level Question Set 41 on Mensuration 3**

**SSC CGL level Solution Set 27 on Mensuration 2**

**SSC CGL level Question Set 27 on Mensuration 2**

**SSC CGL level Solution Set 26 on Mensuration 1**

**SSC CGL level Question Set 26 on Mensuration 1**