Tag: hollow cylinder

Questions Related to hollow cylinder

What will be the volume of a sphere of diameter $15\ cm$? (Correct up to $2$ decimal place)

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

  1. $1436.76\ {cm}^{3}$

  2. $1767.15\ {cm}^{3}$

  3. $14137.17\ {cm}^{3}$

  4. $4188.79\ {cm}^{3}$

Show answer
Correct Option: B
Explanation:

The Volume of a sphere$=\dfrac{4}{3}\pi \ \text{R}^{3}$
Here Radius $R=7.5 \ cm$
On solving We get Volume$=1767.15\ {cm}^{3}$ 

What will be the radius of a sphere whose surface area is 616 $cm^{2}$? (Use $\pi=\dfrac{22}{7}$)

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

  1. $6$ cm

  2. $7$ cm

  3. $8$ cm

  4. $9$ cm

Show answer
Correct Option: B
Explanation:

Radius $=\dfrac{1}{2}\times\sqrt{\dfrac{\text{surface area}}{\pi}}$
on solving we get radius $=7$ cm

If volume of sphere is $850$ $m^{3}$ then its radius and surface area are

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

  1. $6m$, $450$ $m^{2}$

  2. $5m$, $560$ $m^{2}$

  3. $2m$, $780$ $m^{2}$

  4. $5.88m$, $434$ $m^{2}$

Show answer
Correct Option: D
Explanation:
Volume of Sphere $=850m^3=\cfrac{4}{3}\pi r^3 \Rightarrow r^3=\cfrac{850\times 3\times 7}{4\times 22}=202.84 \\ \Rightarrow r=\sqrt[3]{202.84}=5.88m$
Surface area $=4\pi r^2=4\times \cfrac{22}{7}\times 5.88\times 5.88 \approx 434m^2$

 If the radius of a sphere is doubled, then what is the ratio of new to the old surface area?

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

  1. $1:2$

  2. $2:1$

  3. $1:4$

  4. $4:1$

Show answer
Correct Option: D
Explanation:

$S _1=4\pi r^2 \ S _2=4\pi (2r)^2=16\pi r^2 \ \cfrac{S _2}{S _1}=\cfrac{16\pi r^2}{4\pi r^2}=\cfrac{4}{1} \Rightarrow 4:1$

A test-tube consists of a hollow cylindrical tube joined to a hemi-spherical bown of the same internal radius. The whole tube holds $350$ cc of water and in the cylindrical portion falls $1$ cm if $19.64$ cc of water is removed. Find the length of the cylindrical portion of the tube. (Take $\pi =$ $22/7$)

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

  1. $12.15$ cm

  2. $16.15 $ cm

  3. $24.15 $ cm

  4. None of these

Show answer
Correct Option: B
Explanation:

Let r cm. be the radius of the hemisphere and h cm be the length of the cylindrical portion.
Volume of water removed $\pi r^2 (1) = 19.64cc$
$\Rightarrow r^2 = 19.64 \times \displaystyle \frac{7}{22}  \Rightarrow r = 2.5 cm$
Volume of the whole tube $= \pi r^2 h + \displaystyle \frac{2}{h} \pi r^3 = 350 c.c.$
$\Rightarrow \pi r^2 \displaystyle \left ( h + \frac{2}{3} r \right ) = 350$
$\Rightarrow \displaystyle \frac{22}{7} \times 2.5^2 \times \left ( h + \frac{2}{3} \times 2.5 \right ) = 350$
$\displaystyle \frac{22}{7} \times 6.25 \times (h+ 1.67) = 350 $
$ \Rightarrow \displaystyle 350 \times \frac{7}{22} \times 6. 25 - 1.67 cm    \Rightarrow h = 16.15 cm$

The height of a hollow cylinder is $14cm$ if external diameter is $16cm$ and total curved surface area of the hollow cylinder is $1320sq.cm$, then its internal diameter is

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

  1. $14cm$

  2. $16cm$

  3. $7cm$

  4. $8cm$

Show answer
Correct Option: C
Explanation:

Given     

external radius $r _2=8$, height of cylinder $h=14$
 we have,


$2\pi h(r _{1}+r _{2})=1320$

$ \implies8+r _1=\displaystyle \frac{1320\times7}{2\times22\times14}$

$\implies r _1=7cm$

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. $38808 c{m^2}$

Show answer
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

Show answer
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. $18680cm^3$

Show answer
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. $9:20$

Show answer
Correct Option: A