Tag: volume of cylinder

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

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

  1. $2800$ ${ cm }^{ 3 }$
  2. $12320$ ${ cm }^{ 3 }$
  3. $13202$ ${ cm }^{ 3 }$
  4. $13220$ ${ cm }^{ 3 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. $32\pi$
  2. $16\pi$
  3. $8\pi$

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

Volume V = pi * r^2 * h. Given r + h = 6, then h = 6 - r. V(r) = pi * r^2 * (6 - r) = pi * (6r^2 - r^3). To maximize, V'(r) = pi * (12r - 3r^2) = 0. So 3r(4 - r) = 0, r = 4. Then h = 2. Max Volume = pi * 4^2 * 2 = 32 * pi.

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

  1. $1:4$
  2. $1:3$
  3. $3:1$
  4. $2:5$
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 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
$\dfrac{V _1}{V _2}=\left(\dfrac{r _1}{r _2}\right)^2\left(\dfrac{h _1}{h _2}\right)$

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

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

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

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.
In a cylinder, if radius is halved and height is doubled, the volume will be?

  1. Same

  2. Doubled

  3. Halved

  4. Four times
Reveal answer Fill a bubble to check yourself
C 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
$\Rightarrow$  $r _2=\dfrac{1}{2}r _1,$  $h _2=2h _1$
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 $Halved$

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 radius of a cylinder is doubled and the height remains same, the volume will be?

  1. Doubled

  2. Halved

  3. Same

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