Tag: maths

Questions Related to maths

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 :

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

  1. $2587.2 c{m^2}$

  2. $3080 c{m^2}$

  3. $25872 c{m^2}$

  4. $38808 c{m^2}$

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Correct Option: B
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$=2\pi\,r\left(r+h\right)=2\times\dfrac{22}{7}\times 14\left(14+21\right)=2\times\dfrac{22}{7}\times 14\times 35=140\times 22=3080\ sq.cm$

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

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

  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

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Correct Option: A

Find the volume of a solid cylinder whose radius is $14$cm and height $30$cm

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

  1. $18380cm^3$

  2. $18480cm^3$

  3. $18580cm^3$

  4. $18680cm^3$

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Correct Option: A

the radii of two cylinders are in the ratio 2:3 and their height are in the ratio 5:3. ratio of their volume

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

  1. $20:27$

  2. $10:9$

  3. $18:13$

  4. $9:20$

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Correct Option: A

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

Show answer
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. $2:5$

Show answer
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