Tag: area and volume of cylinder

Questions Related to area and volume of cylinder

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 $\pi,\, 3\displaystyle \frac{1}{7}.$

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

  1. 1.5

  2. 1.2

  3. 1.4

  4. 1.6

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Correct Option: A
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 $V=22 ,R=2 ,L=4 , \pi = 3\tfrac{1}{7}= \frac{22}{7}$

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

An iron pipe $20\space cm$ long has exterior diameter equal to $25\space cm$. If the thickness of the pipe is $1\space cm$, find the whole surface area of the pipe.

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

  1. $3167\space cm^2$

  2. $3160\space cm^2$

  3. $3068\space cm^2$

  4. $3268\space cm^2$

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Correct Option: A
Explanation:

TSA of pipe $=$ $2\pi h(R+r)+2\pi ({ R }^{ 2 }-{ r }^{ 2 })$


                     $=$ $2\times \dfrac { 22 }{ 7 } \times 20(12.5+11.5)+2\times \dfrac { 22 }{ 7 } \left( { \left( 12.5 \right)  }^{ 2 }-{ \left( 11.5 \right)  }^{ 2 } \right) $


                     $=$ $\dfrac { 44\times 480 }{ 7 } +\dfrac { 44\times 24 }{ 7 } $

                    $ =$ $\dfrac { 21120 }{ 7 } +\dfrac { 1056 }{ 7 } =\dfrac { 22176 }{ 7 } $

                     $=$ $3167$ ${ cm }^{ 2 }$

The diameters of two cylinders are in the ratio of 2:1 and their volumes are equal. The ratio of their heights will be _________.

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

  1. 1:6

  2. 1:2

  3. 1:4

  4. 3:4

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Correct Option: C
Explanation:
Let the diameter of the given two cylinders are $2x$ and $x$, 
so the radius of these cylinders are $x$ and $0.5 x$ respectively. 

Let the height of these cylinders are $ h _1$ and $ h _2$ respectively.

Given $ πx^2h _1=π(0.5x)^2h _2 $

$∴\dfrac{h _1}{h _2}=\dfrac{(0.5)^2}{1}=\dfrac 14$

$1:4.$

If the volume of a cylinder is $448\pi:cm^3$ and height 7 cm, its total surface area will be ______________.

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

  1. $352:cm^2$

  2. $754.28:cm^2$

  3. $724.64:cm^2$

  4. $354:cm^2$

Show answer
Correct Option: B
Explanation:
Let the radius of cylinder is $r$ cm and height of this is $7$ cm.

Given, volume of cylinder
$=πr^2h$

$448π=πr^2×7⟹r2=64⟹r=8$ cm

∴  Required total surface area of cylinder
$=2πr(r+h)=2π×8(8+7)$

$=2×\dfrac {22} 7×8×15 $

$=754.28$ $cm^2$

200 wooden balls each of diameter 70 mm are to be painted Find the cost of painting these balls at 10 paise/$\displaystyle cm^{2}$

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

  1. Rs.3080

  2. Rs.2771

  3. Rs.4000

  4. Rs.7000

Show answer
Correct Option: A
Explanation:

Total surface area of 200 balls of $\displaystyle \frac{35}{10}$ cm radius will be $\displaystyle 200\times 4\times \frac{22}{7}\times \frac{35}{10}\times \frac{35}{10}$ mm
The cost will be Rs $\displaystyle \frac{200\times 4\times 22\times 35\times 35}{7\times 10\times 10\times 100}$ which simplifies to Rs 3080

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

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

  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 $

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Correct Option: C
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

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

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

  1. 1 : 2

  2. 2 : 1

  3. 1 : 1

  4. 1 : 3

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Correct Option: C
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

A hollow sphere of internal and external radii 3 cm and 4 cm respectively is malted into a cylinder of diameter 37 cm The height of the cylinder is

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

  1. 2 cm

  2. 2.5 cm

  3. 3 cm

  4. none

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Correct Option: D
Explanation:

Given the external  radius of hollow sphere is 4 cm and internal radius 3 cm 

Then volume of metal used=$\frac{4}{2}\pi (R^{2}-r^{2})=\frac{4}{3}\pi \left ( (4)^{2}-(3)^{2} \right )=\frac{4}{3}\pi (16-9)=\frac{4}{3}7\pi $
The diameter of cylinder 37 cm 
Radius of cylinder is =18.5 cm
Volume of cylinder=$\pi r^{2}h=\pi (18.5)^{2}h$
But cylinder made by metal of hollow sphere
$\pi (18.5\times 18.5)h=\frac{4}{3}7\pi \Rightarrow h=\frac{4\times 7}{3\times 18.5\times 18.5}\Rightarrow \Rightarrow h=0.027 cm$

A cistern $6$ m long and $4$ m wide contains water to a depth of $1.25$ m. What is the area of wetted surface?

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

  1. $40$ sq. m

  2. $45$ sq. m

  3. $49$ sq. m

  4. $73$ sq. m

Show answer
Correct Option: D
Explanation:

Given, $l = 6, b = 4$

Also given depth i.e., $ h = 1.25$
Area of the wetted surface $= 2[lb + bh + hl]$
$=2[(6\times 4)+(4\times 1.25)+(1.25\times 6)]$
$=2[24+5+7.5]$
$= 73$ sq. m
Therefore, the area of wetted surface is $73$ sq. m.

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?

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

  1. $55\pi$

  2. $110\pi$

  3. $150\pi$

  4. None of the above

Show answer
Correct Option: D
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.