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

Mark the correct alternative of the following.
The altitude of a right circular cylinder is increased six times and the base area is decreased one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is?

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

Curved surface area of cylinder $=2\pi r h$


Height is increased to $6$ times $=6h$


Base area is decreased to $\left(\dfrac{1}{9}th\right)$ 

i.e. $\pi (r{^{\prime}})^2=\dfrac{1}{9}\pi r^2\Rightarrow r^{\prime}=\dfrac13r $

Now,
New curved surface area $=2\pi\times\dfrac{1}{3}r\times 6h$

                                           $=2\times(2\pi r h)$
$\therefore$  Lateral surface area becomes twice.

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

If the volume of a vessel in the form of a right circular cylinder is 448 $\pi\, cm^{3}$ and its height is 7 cm, then the curved surface area of the cylinder is

  1. $224\, \pi\, cm^{2}$
  2. $212\, \pi\, cm^{2}$
  3. $112\, \pi\, cm^{2}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of a Cylinder of Radius $R$ and height $h$ $ = \pi { R }^{ 2 }h $
$\therefore $ volume of the given cylinder $ =\pi \times {R}^{2} \times 7  = 448 \pi  {cm}^{3} $

$ {R}^{2} = 64 $

$ R = 8 cm $  

Curved surface area of a cylinder of radius "$R$" and height "$h$" $ = 2\pi Rh$

$\therefore$ curved surface area of the given cylinder $ = 2\times \pi \times 8\times 7 =  112 \pi   \  cm^2 $

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

A rectangular sheet of width $14$ m is rolled along its width and is converted to form a cylinder. Find the radius of cylinder.

  1. $\displaystyle \frac { 22 }{ 49 } $
  2. $\displaystyle \frac { 44 }{ 29 } $
  3. $\displaystyle \frac { 49 }{ 22 } $

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Curved surface area of cylinder$=100m^2$

$\therefore 2 \pi r h = 100$
Here, width of the rectangle = height of the cylinder.
$\therefore h=14m$

$\therefore 2 \times \dfrac {22}{7} \times r \times 14 = 100$

$ \therefore r = \dfrac {100 \times 7}{2 \times 22 \times 14}$

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

In a cylinder, if the radius is halved and height is doubled, the curved surface area will 

  1. remain same

  2. increase

  3. decrease

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of cylinder $\displaystyle \pi { r }^{ 2 }h$
Now, if $\displaystyle r=\frac { r }{ 2 } & h=h2$
New CSA $\displaystyle =2\pi rh$
$\displaystyle =2\pi \left( \frac { r }{ 2 }  \right) \times \left( h\times 2 \right) $
$\displaystyle =2\pi rh$
It will remain same

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

The inner diameter of a circular well is $3.5$ m. It is $10$ m deep. Find the cost of plastering this curved surface at the rate of Rs. $40$ per m$^2$.

  1. Rs. $4000$
  2. Rs. $4400$
  3. Rs. $4500$
  4. Rs. $4800$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given diameter of well is $3.5$ m and depth is $10$ m and cost of plastering is Rs. $40$ per sq m.

Then radius of well $=\dfrac{3.5}{2}=1.75$ m
And height of well $=10$ m
Then curved surface area of well $=$ $2\pi rh=2\times \dfrac{22}{7}\times 1.75\times 10$
$=$ $2\times 22\times 0.25\times 10=110 m^{2}$
Then cost of plastering curved surface area $=$ $110\times 40=$ Rs. $4400$.

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 $7 cm$ and its radius is $3.5 cm$. Then the surface area is

  1. $231{ cm }^{ 2 }$
  2. $154{ cm }^{ 2 }$
  3. $308{ cm }^{ 2 }$
  4. $115.5{ cm }^{ 2 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given : radius $r=3.5 cm$ and height $h=7cm$

Surface area of a hollow cylinder $=2\pi r(h+r)$
                                                        $=2\times 3.14\times 3.5(7+3.5)$
                                                        $=230.79cm^2\approx 231$
$\therefore$ Surface area $=231cm^2$.

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

A flower pot is in the form of a hollow cylinder with a closed base with inner radius $2cm$ and outer radius $4cm$ . The height of the flower pot is $10cm$ . If the pot has to be polished find the cost of polishing if the cost of polishing per ${cm}^{2}$ is $Rs.2$.

  1. $Rs.276.32$
  2. $Rs.275$
  3. $Rs.270$
  4. $Rs.278.64$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We have to first find the total surface area of the flower pot.
Outer radius $=4cm$
Inner radius $=2cm$
Height of flower pot $=10cm$
Total surface area $=A=2\pi Rh+2\pi rh+\pi { { R }^{ 2 } }+\pi { { r }^{ 2 } }$
$A=2\pi (R+r)h+\pi ({ R }^{ 2 }+{ r }^{ 2 })\ A=2\pi (4+2)2+\pi (16+4)\ A=24\pi +20\pi =44\pi \ A=40\pi =44\times 3.14=138.16{ cm }^{ 2 }$
Cost of fabrication per ${cm}^{2}$ $=Rs.2$
Total cost of fabrication $==138.16\times 2=Rs.276.32$

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

What will be the Inner surface area of a spherical shell of inner radius $15\ cm$ and outer radius $16\ cm$? (Correct upto 2 decimal places)

  1. $706.86\ {cm^2}$
  2. $804.25\ {cm^2}$
  3. $2827.43\ {cm^2}$
  4. $3216.99\ {cm^2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Inner surface area of a spherical shell = 4 * pi * r^2. With r = 15, Area = 4 * 3.14159 * 225 = 2827.43 cm^2.

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

A hemispherical bowl has inner radius $5cm$ and outer radius $6cm$. What will be the volume of solid enclosed between the two hemispheres? (Correct upto 2 decimal places)

  1. $904.78 \ {cm}^{3}$
  2. $523.60 \ {cm}^{3}$
  3. $381.18 \ {cm}^{3}$
  4. $190.59 \ {cm}^{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The volume of hemispherical shell$= \dfrac{2}{3}\pi*R^{3}-\dfrac{2}{3}\pi*r^{3}$
where R and r are the outer and inner radius of the hemisphere
On solving the equation we get Volume$= 190.59 \ {cm}^{3}$

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

The surface area of a solid spherical ball of diameter $10\ cm$ is equal to :

  1. $25\pi\ {cm}^2$
  2. $50\pi\ {cm}^2$
  3. $100\pi\ {cm}^2$
  4. $200\pi\ {cm}^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given: Diameter of the sphere $= 10\ cm$
Hence, Radius ($r$) of the sphere will be $5\ cm$

We know that, 
Surface area of the sphere is $4\pi r^2$
Therefore, Area will be $4\pi (5)^2 = 100\pi\ {cm}^2$

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

What will be the Inner and Outer radius of a spherical shell of inner surface area $452.39\ {cm}^2$ and outer surface area $804.25\ {cm}^2$ ? (Surface areas are accurate upto 2 decimal places)

  1. $6 \ cm, 7 \ cm$
  2. $7 \ cm, 8 \ cm$
  3. $6 \ cm, 8 \ cm$
  4. $7 \ cm, 9\ cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Inner surface area$=4\pi { \left( inner\quad radius \right)  }^{ 2 }$
$\Rightarrow 4\pi { \left( { r } _{ 1 } \right)  }^{ 2 }=452.39cm^{2}\Rightarrow { r } _{ 1 }^{ 2 }=\cfrac { 452.39\times 7 }{ 4\times 22 } =35.99$
$\Rightarrow { r } _{ 2 }=\sqrt { 35.99 } =5.99\approx 6cm$
Outer surface area$=4\pi { \left( outer\quad radius \right)  }^{ 2 }$
$\Rightarrow 4\pi { \left( { r } _{ 2 } \right)  }^{ 2 }=804.25㎠\Rightarrow { r } _{ 2 }^{ 2 }=\cfrac { 804.25\times 7 }{ 4\times 22 } =63.97$
$\Rightarrow { r } _{ 2 }=\sqrt { 63.97 } =7.99\approx 8cm$
Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

The value of radius for which the numerical value of total surface area of a sphere and the volume of sphere are equal, will be:(Consider the units of volume and surface area as ${cm}^3\  \text{and}\ {cm}^2$)

  1. $1cm$
  2. $2cm$
  3. $3cm$
  4. $4cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let radius of sphere be $'r'㎝$, then
TSA of sphere=volume of sphere
$\Rightarrow 4\pi { r }^{ 2 }=\cfrac { 4 }{ 3 } \pi { r }^{ 3 }\Rightarrow r=3cm$
Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

The increase in the total surface area of a sphere of Radius ${R}$ when it is cut to make two hemispheres of same Radius will be equal to:

  1. $5\ \pi{R}^2$
  2. $4\ \pi{R}^2$
  3. $3\ \pi{R}^2$
  4. $2\ \pi{R}^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Total surface area of sphere$=4\pi { R }^{ 2 }$
TSA of hemisphere=CSA of hemisphere+CSA of circle
$=2\pi { R }^{ 2 }+\pi { R }^{ 2 }=3\pi { R }^{ 2 }$
$\therefore $TSA of two hemisphere$=2\times 3\pi { R }^{ 2 }=6\pi { R }^{ 2 }$
Therefore, increase in TSA$=6\pi { R }^{ 2 }-4\pi { R }^{ 2 }=2\pi { R }^{ 2 }$
Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

The perimeter of a sector of a circle is $56$ cms and the area of the circle is $64\pi$ sq. cms  Find the area of sector.

  1. $360cm^2$
  2. $160cm^2$
  3. $260cm^2$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area $= \pi r^{2}=64\pi cm^{2}$  


$\Rightarrow r=8cm$ 


perimeter $=2r+r\theta $ 

perimeter of sector $=r(\theta +2)=56cm$ 

$\Rightarrow \theta =5rad$ 

Area of sector $=\dfrac{r^{2}\theta }{2}=\dfrac{64}{2}\times 5cm^{2}$

                        $=160cm^{2}$

Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

What is the area of the sector of a circle, whose radius is $6\ m$ when the angle at the centre is $42^{\circ}$?

  1. $13.2\ m^{2}$
  2. $14.2\ m^{2}$
  3. $13.4\ m^{2}$
  4. $14.4\ m^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of sector $=$ $\dfrac { \theta  }{ { 360 }^{ 0 } } \times \pi { r }^{ 2 }=\dfrac { { 42 }^{ 0 } }{ { 360 }^{ 0 } } \times \dfrac { 22 }{ 7 } \times 6\times 6=13.2{ m }^{ 2 }$