Question

A hollow cylindrical pipe is $21$cm long. If its outer and inner diameters are $10$ cm and $6$cm respectively, then the volume of the metal used in making the pipe is-(Take$\pi = \dfrac{{22}}{7}$ )
A.$1048{\text{ c}}{{\text{m}}^3}$
B.$1056{\text{ c}}{{\text{m}}^3}$
C.$1060{\text{ c}}{{\text{m}}^3}$
D.$1064{\text{ c}}{{\text{m}}^3}$

Answer 1

Hint: Use the formula of volume of cylinder =$\pi {R^2}h$ where R=radius of the cylinder, h is the height of the cylinder to find the volume of the inner cylinder and the volume of the outer cylinder. Then subtract the volume of inner radius from outer radius to find the volume of metal used in the making of pipe.

Complete step-by-step answer:
Given, the height of the hollow cylinder h=$21$cm
The inner diameter of hollow cylinder=$6$cm
And the outer diameter=$10$ cm

Then we have to find the volume of the metal used in making the pipe.
We know that Radius=$\dfrac{{Diameter}}{2}$
Then inner radius r=$\dfrac{6}{2} = 3$cm
And the outer radius R=$\dfrac{{10}}{2} = 5$cm
Then volume of inner cylinder=$\pi {r^2}h$
On putting the given values we get,
$ \Rightarrow $ Volume of inner cylinder=$\dfrac{{22}}{7} \times {\left( 3 \right)^2} \times 21$
On solving we get,
$ \Rightarrow $Volume of inner cylinder=$22 \times 9 \times 3 = 594$${\text{c}}{{\text{m}}^3}$
And the volume of outer cylinder=$\pi {R^2}h$
On putting the given values we get,
$ \Rightarrow $Volume of outer cylinder=$\dfrac{{22}}{7} \times {\left( 5 \right)^2} \times 21$
On solving we get,
$ \Rightarrow $Volume of outer cylinder=$22 \times 25 \times 3 = 1650$${\text{c}}{{\text{m}}^3}$
Now the volume of metal used in the making of pipe=Volume of outer cylinder-volume of inner cylinder
On putting the values we get,
The volume of metal used in the making of pipe=$1650 - 594$
The volume of metal used in the making of pipe=$1056$ ${\text{c}}{{\text{m}}^3}$

Answer- The correct answer is B.

Note: You can directly use the formula of hollow cylinder which is given as-
Volume of hollow cylinder=$\pi h\left( {R - r} \right)$ where h is the height of the cylinder, R is the outer radius and r is the inner radius to find the volume of metal used to make the cylindrical pipe because the volume of metal used will be equal to the volume of the hollow cylinder.