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 area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

The volume, V $cm^{2}$, of a hollow cylindrical pipe of length $l$ cm, outer radius R cm and inner radius r cm is given by the formula : $V\, =\, \pi\, (R^{2}\, -\, r^{2}).\, l$

Find r, if $V\, =\, 22,\, R\, =\, 2,\, l\, =\, 4$ and $\pi,\, 3\displaystyle \frac{1}{7}.$

  1. 1.5

  2. 1.2

  3. 1.4

  4. 1.6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given $V= \pi \left ( R^{2}-r^{2} \right )l$

$V= \pi  R^{2}-\pi r^{2} l$

$\pi r^{2}l= \pi R^{2}l-V$


$ r^{2}= \dfrac{\pi R^{2}l-V}{\pi l}$

$\therefore  r= \sqrt{\dfrac{\pi R^{2}l-V}{\pi l}}$

Given $V=22 ,R=2 ,L=4 , \pi = 3\tfrac{1}{7}= \frac{22}{7}$

$\therefore r= \sqrt{\dfrac{\frac{22}{7}\times 4\times 4-22}{\dfrac{22}{7}\times4}}= \sqrt{\dfrac{352-154}{88}}= \sqrt{\dfrac{198}{88}}= \sqrt{\dfrac{9}{4}}= 1.5$

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

A rectangular paper of dimensions 6 cm and 3 cm is rolled to form a cylinder with height equal to the width of the paper, then its base radius is

  1. $ \displaystyle \frac{6}{\pi }cm $
  2. $ \displaystyle \frac{3}{2\pi }cm $
  3. $ \displaystyle \frac{6}{2\pi }cm $
  4. $ \displaystyle \frac{9}{2\pi }cm $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The length of the rectangle become the circumference of the base of the cylinder 

$\therefore 2\pi r=6\Rightarrow r=\frac{6}{2\pi }$ cm

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

The curved surface of a circular cylinder of height 'h' and the curved surface area of the cone of slant height 2 'h' having the same circular base are in the ratio of

  1. 1 : 2

  2. 2 : 1

  3. 1 : 1

  4. 1 : 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the base radius of cone and circular cylinder is r and height of circular cylinder is h and height of cone 2h

Then Curved surface area of circular cylinder =$2\pi rh$
And curved surface area of cone=$\pi r(2h)=2\pi rh$
So ratio of Curved surface area of circular cylinder : curved surface area of cone :: $2\pi r(h)=2\pi rh$ : $2\pi rh$=1:1

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

The outer and inner diameters of a circular pipe are $6$ cm and $4$ cm respectively. If its length is $10$ cm then what is the total surface area in square centimetres?

  1. $55\pi$
  2. $110\pi$
  3. $150\pi$

  4. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given, outer and inner diameters of circular pipe are $6$ cm and $4$ cm
Therefore, outer and inner radii of a circular pipe are $3$ cm and $2$ cm.
Thus total surface area would be $ 10\times \pi (3^{2} - 2^{2})$ $= 50\pi $ sq. cm.

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

If volume of sphere is $850$ $m^{3}$ then its radius and surface area are

  1. $6m$, $450$ $m^{2}$
  2. $5m$, $560$ $m^{2}$
  3. $2m$, $780$ $m^{2}$
  4. $5.88m$, $434$ $m^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Volume of Sphere $=850m^3=\cfrac{4}{3}\pi r^3 \Rightarrow r^3=\cfrac{850\times 3\times 7}{4\times 22}=202.84 \\ \Rightarrow r=\sqrt[3]{202.84}=5.88m$
Surface area $=4\pi r^2=4\times \cfrac{22}{7}\times 5.88\times 5.88 \approx 434m^2$
Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

The height of a hollow cylinder is $14cm$ if external diameter is $16cm$ and total curved surface area of the hollow cylinder is $1320sq.cm$, then its internal diameter is

  1. $14cm$
  2. $16cm$
  3. $7cm$
  4. $8cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given     

external radius $r _2=8$, height of cylinder $h=14$
 we have,


$2\pi h(r _{1}+r _{2})=1320$

$ \implies8+r _1=\displaystyle \frac{1320\times7}{2\times22\times14}$

$\implies r _1=7cm$

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

The ratio between the radius of the base and the height of a cylinder is $2:3$. If its volume is $12936$ cu. cm, the total  surface area of the cylinder is :

  1. $2587.2 c{m^2}$
  2. $3080 c{m^2}$
  3. $25872 c{m^2}$
  4. $38808 c{m^2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
We have $\dfrac{r}{h}=\dfrac{2}{3}\Rightarrow\,h=\dfrac{3r}{2}$

Volume of a cylinder$=\pi{r}^{2}h$

$\Rightarrow\,12936=\dfrac{22}{7}\times{r}^{2}\times \dfrac{3r}{2}$

$\Rightarrow\,12936=\dfrac{11\times 3}{7}{r}^{3}$

$\Rightarrow\,{r}^{3}=\dfrac{12936\times 7}{33}=2744$

$\Rightarrow\,r=\sqrt[3]{2744}=14\ cm$

We have $h=\dfrac{3r}{2}=\dfrac{3\times 14}{2}=21\ cm$

Total Surface area$=2\pi\,r\left(r+h\right)=2\times\dfrac{22}{7}\times 14\left(14+21\right)=2\times\dfrac{22}{7}\times 14\times 35=140\times 22=3080\ sq.cm$
Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

A cylinder and cone of equal base radius and equal height are given. Which of the following statement is true/

  1. Volume of cylinder and cone are equal

  2. Volume of cylinder is one-third of volume of cone

  3. Volume of cone is half of the volume of cylinder

  4. Volume of cone is one-third of volume of cylinder
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The volume of a cylinder is given by V_cyl = pi r^2 h, while the volume of a cone with the same base radius and height is V_cone = (1/3) pi r^2 h. Therefore, the volume of the cone is exactly one-third of the volume of the cylinder.

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

Mark the correct alternative of the following.
In a cylinder, if radius is doubled and height is halved, curved surface area will be?

  1. Halved

  2. Doubled

  3. Same

  4. Four times
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the radius of cylinder be $r$ and height be $h.$

So, the original curved surface area $=2\pi rh$
When, radius is doubled and height is halved,
New curved surface area $=2\pi \times 2r\times \dfrac{h}{2}$

                                           $=2\pi r h$
$\therefore$  New curved surface area $=$ Original surface area.
$\therefore$  There is no change in the curved surface area of the cylinder

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

Mark the correct alternative of the following.
The radius of a wire is decreased to one-third. If volume remains the same, the length will become?

  1. $3$ times
  2. $6$ times
  3. $9$ times
  4. $27$ times
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let $V _1$ and $V _2$ be the volume of the two cylinders with $h _1$ and $h _2$ as their heights.

Let $r _1$ and $r _2$ be their base radius.
It is given that, the radius of a wire is decreased to on-third.
$\therefore$  $r _2=\dfrac{1}{3}r _1$

$\Rightarrow$  $V _1=V _2$             [ Given ]
$\Rightarrow$  $\pi r _1^2 h _1=\pi r _2^2 h _2$

$\Rightarrow$  $r _1^2 h _1=\left(\dfrac{1}{3}r _1\right)^2 h _2$

$\Rightarrow$  $r _1^2 h _1=\dfrac{1}{9} r _1^2 h _2$

$\Rightarrow$  $h _2=9h _1$

$\therefore$  The length will become $9$ times.

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

Mark the correct alternative of the following.
If the height of a cylinder is doubled and radius remains the same, then volume will be?

  1. Doubled

  2. Halved

  3. Same

  4. Four times
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let $V _1$ be the volume of the cylinder with radis $r _1$ and height $h _1,$ then

$\Rightarrow$  $V _1=\pi r _1^2 h _1$            ---- ( 1 )
Now, let $V _2$ be the volume after changing the dimension, then
$\Rightarrow$  $r _2=r _1,$  $h _2=2h _1$
So,
$\Rightarrow$  $V _2=\pi r _2^2h _2$

$\Rightarrow$  $V _2=\pi\times{r _1}^2\times 2h _1$

$\Rightarrow$  $V _2=2\times \pi r _1^2 h _1$
From ( 1 ),

$\Rightarrow$  $V _2=2V _1$

$\therefore$  If the height of a cylinder is doubled and radius remains the same, then volume will be $Doubled.$

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

Mark the correct alternative of the following.
The volume of a cylinder of radius r is $1/4$ of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x?

  1. $\dfrac{x^2}{2\pi}$
  2. $\dfrac{x}{2\sqrt{\pi}}$
  3. $\dfrac{\sqrt{2x}}{\pi}$
  4. $\dfrac{\pi}{2\sqrt{x}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the height of the cylinder be $h.$

Volume of the cylinder $=\pi r^2 h$
Height of the rectangular box $=h$
Since, base is square with side $x.$
Volume of the box $=x\times x\times h=x^2 h$
According to question,
$\Rightarrow$  $\pi r^2  h=\dfrac{1}{4} x^2 h$

$\Rightarrow$  $r^2=\dfrac{1}{4\pi}x^2$
Taking square root on both sides,
$\Rightarrow$  $r=\dfrac{x}{2\sqrt{\pi}}$