# Mensuration – Quiz 4

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# Mensuration – Quiz 4

### Introduction

Mensuration is one of important topic in Quantitative Aptitude Section. In Mensuration – Quiz 4 article candidates can find questions with an answer. By solving this question candidates can improve and maintain, speed, and accuracy in the exams. Mensuration – Quiz 4 questions are very useful for different exams such as IBPS PO, Clerk, SSC CGL, SBI PO, NIACL Assistant, NICL AO, IBPS SO, RRB, Railways, Civil Services etc.

### Q1

A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
A. 10 B. 100 C. 1000 D. 10000

C
Along one edge, the number of small cubes that can be cut
= $\frac{100}{10}$ = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height).
Total number of small cubes that can be cut = 10 $\times$ 10 $\times$ 10 = 1000

### Q2

The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
A. 252 B. 704 C. 352 D. 808

B
In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 $\times$ 2 $\times$ $\frac{22}{7}$ $\times$ 22.4
= 70400 cm = 704 m

### Q3

The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
A. 2 : 5 B. 1 : 5 C. 3 : 5 D. 4 : 5

A
The volume of the cone = $(\frac{1}{3}) \pi {r}^{2}h$
Only radius (r) and height (h) are varying.
Hence, $(\frac{1}{3}) \pi$ may be ignored.
$\frac {{V}_{1}}{{V}_{2}}$ = $\frac {{{r}_{1}}^{2} {h}_{1}}{{{r}_{2}}^{2} {h}_{2}} = \Rightarrow \frac{1}{10} = \frac {{(1)}^{2} {h}_{1}}{{(2)}^{2} {h}_{2}}$
$\frac{{h}_{1}}{{h}_{2}} = \frac {2}{5}$
i.e. ${h}_{1} : {h}_{2}$ = 2 : 5

### Q4

A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
A. 45 B. 18 C. 9 D. 180

C
Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
$\pi {(16)}^{2} \times h = (\frac {4}{3}) \pi {(12)}^{3} \Rightarrow h = 9 cm$

### Q5

The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
A. 81 : 121 B. 9 : 11 C. 729 : 1331 D. 27 : 121

A
Ratio of the sides = $\sqrt [3] {729}$ : $\sqrt [3] {1331}$ = 9 : 11
Ratio of surface areas = ${(9)}^{2} : {(11)}^{2}$ = 81 : 121