Quantitative Aptitude

Mensuration

2,507 Questions
All Direct Formula Application 1067 Shape Transformations 343 Mensuration Ratio Equations 277 Combined & Hollow Solids 247 Successive Percentage Changes 178 Inscribed & Circumscribed Figures 165 Cost Estimation Problems 100 Liquid Pour & Submergence 67 Unit Conversions 35 Path & Border Calculations 17 Time & Work Integration 7 Scale & Model Proportions 2

Mensuration Questions

Multiple choice maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

A hemispherical bowl of internal diameter $36$ cm is full of some liquid. This liquid is to be filled in cylindrical bottles of radius $3$ cm and height $6$ cm, then no. of bottles needed to empty the bowl

  1. $36$
  2. $72$
  3. $18$
  4. $144$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Radius of the bowl $ = \dfrac {36}{2} = 18  cm $

Volume of the bowl $ = \dfrac { 2 }{ 3 }

\pi { r }^{ 3 } = \dfrac {2}{3} \times \pi \times 18 \times 18 \times

18 {cm}^{3} $





Volume

of a Cylinder of Radius "R" and height "h" $ = \pi { R }^{

2 }h $





Hence, Volume of one cylindrical bottle, $ = \pi \times 3 \times 3 \times  6 $

Hence, number of bottled required $

= \dfrac {Volume  of  bowl} {Volume  of  each  bottle} = \dfrac{\dfrac {2}{3} \times \pi \times 18 \times 18 \times

18}{ \pi \times 3 \times 3 \times 

6} = 72 $

Multiple choice maths how big? how heavy? measuring volume volume of solids volume of cube and cuboid

A sphere of radius 2 cm is put into water contained in a cylinder of radius 4 cm. If the sphere is completely immersed, the water level in the cylinder rises by __________________.

  1. Two cm
  2. $\displaystyle\frac{1}{3}\:cm$
  3. $\displaystyle\frac{1}{2}\:cm$
  4. $\displaystyle\frac{2}{3}\:cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 2^3 = (32/3) * pi. Volume of water rise in cylinder = pi * R^2 * h = pi * 4^2 * h = 16 * pi * h. Equating: (32/3) * pi = 16 * pi * h, so h = 32 / (3 * 16) = 2/3 cm.

Multiple choice maths perimeter, area and volume volume of prism and pyramid surface areas and volumes of solids recall the surface areas and volumes of different solid shapes

The base of the right pyramid is a square of side 16 cm and height 15 cm. Its volume $(cm^{3})$ will be

  1. $3840$
  2. $1920$
  3. $1280$
  4. $960$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area of the base $=$ $(16 \times 16) cm^2$
Volume of the pyramid $=$ $\frac{1}{3} \times B h$
Volume of the pyramid $=$ $\frac{1}{3}\left ( 16\times 16 \right )\times 15$
$= 1280 cm^2$

Multiple choice maths perimeter, area and volume volume of prism and pyramid surface areas and volumes of solids recall the surface areas and volumes of different solid shapes

A regular square pyramid is $3$ m height and the perimeter of its base is $16$ m. Find the volume of the pyramid.

  1. <span class="MathJax_Preview"><span class="MathJax"><span class="math"><span class="mrow"><span class="mn">12<span class="MJX_Assistive_MathML">12 $cu. m$
  2. <span class="MathJax_Preview"><span class="MathJax"><span class="math"><span class="mrow"><span class="mn">14<span class="MJX_Assistive_MathML">14 $cu. m$
  3. <span class="MathJax_Preview"><span class="MathJax"><span class="math"><span class="mrow"><span class="mn">16<span class="MJX_Assistive_MathML">16 $cu. m$
  4. <span class="MathJax_Preview"><span class="MathJax"><span class="math"><span class="mrow"><span class="mn">18<span class="MJX_Assistive_MathML">18 $cu. m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, height of regular square pyramid is $3$ m and the perimeter of its base is $16$ m

Let the base side of pyramid is $l$ m
Then perimeter of base $=4a=16$
So, $ a=4$
Then volume of pyramid $=$ $\dfrac{1}{3}l^{2}h=\dfrac{1}{3}\times (4)^{2}\times 3=16 $ $cu. m$

Multiple choice maths perimeter, area and volume volume of prism and pyramid surface areas and volumes of solids recall the surface areas and volumes of different solid shapes

The length of the base of a square pyramid is $2\ cm$ and the height is $6\ cm$. Calculate the volume.

  1. $8\ cm^3$
  2. $6\ cm^3$
  3. $4\ cm^3$
  4. $2\ cm^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of square pyramid  $=\dfrac { 1 }{ 3 } \times { a }^{ 2 }\times h=\dfrac { 1 }{ 3 } \times 2\times 2\times 6=8{ cm }^{ 3 }$

Multiple choice maths surface areas and volumes volume of a sphere problems involving volume of combined solids application of surface area and volume of solids

A metallic solid cone is melted and cast into a cylinder of the same base as that of the cone. If the height of the cylinder is $7\;cm$, what was the height of the cone?

  1. $20\;cm$
  2. $21\;cm$
  3. $22\;cm$
  4. $12\;cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cone $=$ Volume of cylinder

$\dfrac { 1 }{ 3 } \pi { r } _{ 1 }^{ 2 }{ h } _{ 1 }=\pi { r } _{ 2 }^{ 2 }{ h } _{ 2 }$
$\Rightarrow \quad \dfrac { 1 }{ 3 } \times { r }^{ 2 }\times { h } _{ 1 }={ r }^{ 2 }\times 7\quad \left[ { r } _{ 1 }={ r } _{ 2 }=r \right] $
                  $\Rightarrow \quad { h } _{ 1 }=7\times 3=21cm$
Therefore, height of cone is $21$ cm.

Multiple choice maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

$r$ is the radius and $l$  is the length of an arc. The area of a sector is ______.

  1. $\dfrac { 1 } { 2 } r l$
  2. $\dfrac { 3 } { 2 } r ^ { 2 } l$
  3. $\dfrac { 4 } { 3 } r l$
  4. $\dfrac { 3 } { 2 } r l$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} Area\, of\, a\, \sec  tor\, =\dfrac { 1 }{ 2 } { r^{ 2 } }\theta  \ =\dfrac { 1 }{ 2 } \times r\times r\theta  \ =\dfrac { 1 }{ 2 } \times r\times l \ Hence,\, option\, A\, is\, \, the\, \, correct\, \, answer. \end{array}$

Multiple choice maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

Consider a circle with unit radius. There are seven adjacent sectors, $S _1, S _2, S _3, ............ S _7$, in the circle such that their total area is $\dfrac {1}{8}$ of the area of the circle. Further, the area of the $j^{th}$ sector is twice that of the $(j-1)^{th}$ sector, for $j$ $=$ $2, ........... 7$. What is the area of sector $S _1?$

  1. $\displaystyle \frac{\pi }{508}$
  2. $\displaystyle \frac{\pi }{2040}$
  3. $\displaystyle \frac{\pi }{1016}$
  4. $\displaystyle \frac{\pi }{1524}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the area of thesector S$ _1$ be x units. Then, the area of the corresponding sectors shall be 2x, 4x, 8x, 16x, 32x and 64x. The total area then shall be 127x units. This is $\displaystyle \frac{1}{8}$ of the total area of the circle. 

Hence, the total area of the circle will be $127x \times 8 = 1,016 x\ units.$
$\Rightarrow 1016 x = \pi (1)^2 \Rightarrow x = \pi/1016$
Hence area of sector $S _1 $ is $\pi / 1016$

Multiple choice introduction to ratio and percentages comparing quantities maths

If the diameter of a sphere is decreased by $25\%$, by what percent does its curved surface area decrease?

  1. $43.75\%$
  2. $21.88\%$
  3. $50\%$
  4. $25\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Curved surface area of sphere$=4\pi r^2$
diametre after decreases by $25\%$
$A _D=\pi d^2$
$d _1=\displaystyle\frac{75}{100}d=\frac{3d}{4}$
$A _1=\pi \left(\displaystyle\frac{3d}{4}\right)^2=\frac{9}{16}\pi d^2$
$\%$ decrease=$\displaystyle\frac{\displaystyle\frac{9}{16}\pi d^2-\pi d^2}{\pi d^2}\times 100=-43.75\%$

Multiple choice maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

When the circumference of a circle decreases from $3\, \pi$ to $\pi$ , its area decreases by

  1. $16\, \displaystyle \frac{2}{3}$ %
  2. $66\, \displaystyle \frac{2}{3}$ %
  3. $88\, \displaystyle \frac{8}{9}$ %
  4. $12\, \displaystyle \frac{1}{2}$ %
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio of circumference = 3 : 1
Ratio of radii = 3 : 1
$\therefore$ ratio of areas $=\, 3^2\, : 1^2\, 9\, :\, 1$
% decrease in area $=\, \displaystyle \frac{8}{9}\, \times\, 100$
$=\, 88\, \displaystyle \frac{8}{9}$ %