Tag: hollow cylinder

Questions Related to hollow cylinder

A solid cylinder has a total surface area of $231cm^2$. Its curved surface area. Find the volume of the cylinder?

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

  1. $270cm^3$

  2. $269.5cm^3$

  3. $256.5cm^3$

  4. $289.5cm^3$

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Correct Option: A

Volume of a cylinder when $d=7\ cm$ and $h=3\ cm$

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

  1. $118\ cm^{3}$

  2. $115.5\ cm^{3}$

  3. $155.5\ cm^{3}$

  4. $808.5\ cm^{3}$

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Correct Option: A

A cylindrical pipe is made from a metal sheet of length 88 cm and breadth 20 cm. What is the volume of this pipe?

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

  1. $2800$ ${ cm }^{ 3 }$

  2. $12320$ ${ cm }^{ 3 }$

  3. $13202$ ${ cm }^{ 3 }$

  4. $13220$ ${ cm }^{ 3 }$

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Correct Option: A
Explanation:

We have,

Length $l=88\,cm.$

Breadth$b=20\,cm.$

Volume $=?$

Volume of cylindrical pipe $=\pi {{r}^{2}}h$

We know that,

$ circumfrance=Breadth=2\pi r $

$ 2\pi r=20 $

$ \pi r=10 $

$ r=\dfrac{10}{\pi } $

$ r=\dfrac{10}{\dfrac{22}{7}} $

$ r=\dfrac{70}{22} $

$ r=\dfrac{35}{11}\,\,cm. $

Then,

Volume of cylindrical pipe $V=\pi {{r}^{2}}h$

$ V=\dfrac{22}{7}\times \dfrac{35}{11}\times \dfrac{35}{11}\times 88 $

$ V=2\times 5\times 35\times 8 $

$ V=80\times 35 $

$ V=2800\,c{{m}^{3}} $

Hence, this is the answer.

If sum of radius and height of a cylinder is 6, then its maximum volume is 

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

  1. $32\pi$

  2. $16\pi$

  3. $8\pi$

  4. None of these

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Correct Option: A

Mark the correct alternative of the following.
Two cylindrical jars have their diameters in the ratio $3:1$, but height $1:3$. Then the ratio of their volumes is?

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

  1. $1:4$

  2. $1:3$

  3. $3:1$

  4. $2:5$

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Correct Option: C
Explanation:

Let $V _1$ and $V _2$ be the volume of the two cylinders with radius $r _1$ and height $h _1$, and radius $r _2$ and height $h _2.$

$\dfrac{2r _1}{2r _2}=\dfrac{3}{1}$ and $\dfrac{h _1}{h _2}=\dfrac{1}{3}$             [ Given ]
So,
$V _1=\pi r _1^2h _1$           ----- ( 1 )
Now,
$V _2=\pi r _2^2h _2$            ---- ( 2 )
From equation ( 1 ) and ( 2 ), we get
$\dfrac{V _1}{V _2}=\left(\dfrac{r _1}{r _2}\right)^2\left(\dfrac{h _1}{h _2}\right)$

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

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

$\Rightarrow$  $\dfrac{V _1}{V _2}=\dfrac{3}{1}$

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

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

  1. Halved

  2. Doubled

  3. Same

  4. Four times

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Correct Option: C
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

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?

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

  1. $3$ times

  2. $6$ times

  3. $9$ times

  4. $27$ times

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Correct Option: C
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.

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

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

  1. Doubled

  2. Halved

  3. Same

  4. Four times

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Correct Option: A
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 $Doubled.$

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

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

  1. Same

  2. Doubled

  3. Halved

  4. Four times

Show answer
Correct Option: C
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
$\Rightarrow$  $r _2=\dfrac{1}{2}r _1,$  $h _2=2h _1$
So,
$\Rightarrow$  $V _2=\pi r _2^2h _2$

$\Rightarrow$  $V _2=\pi\times\left(\dfrac{r _1}{2}\right)^2\times 2h _1$

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

$\Rightarrow$  $V _2=\dfrac{1}{2}V _1$

$\therefore$  In a cylinder, if radius is halved and height is doubled, the volume will be $Halved$

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

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

  1. Doubled

  2. Halved

  3. Same

  4. Four times

Show answer
Correct Option: D
Explanation:

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

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

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

$\Rightarrow$  $V _2=4\times \pi r _1^2 h _1$
From ( 1 ),
$\therefore$  $V _2=4V _1$
Hence, If the radius of a cylinder is doubled and the height remains same, the volume will be Four times.