Question

The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. Find the volume of the cylinder. (use $\pi = \dfrac{{22}}{7}$)

Answer 1

Hint: If r and h are the radius and the height of the cylinder then the volume of the cylinder is given as $\pi {r^2}h$. In this question the value of height is given. In order to get the value of r, we will use the simple formula of circumference of the base of a cylinder as $2\pi r$.

Complete step-by-step answer:

Given that
$h = 25cm$ and circumference is \[132cm.\]

Let “r” be the radius of the given cylinder.

As we know that circumference of the circle is given as $2\pi r$

By putting the value of circumference, we get
$
   \Rightarrow 132 = 2\pi r \\
   \Rightarrow r = \dfrac{{132}}{2} \times \dfrac{7}{{22}} \\
   \Rightarrow r = 21cm \\
 $

Therefore, volume of a cylinder = $\pi {r^2}h.$

By putting the value of r and h, we get

Volume of cylinder
$
   = \pi {r^2}h \\
   = \dfrac{{22}}{7} \times {21^2} \times 25 \\
   = 34,650c{m^3} \\
 $

Hence, the volume of the cylinder is $34,650c{m^3}$.

Note: In order to solve these types of questions, remember all the formulas related to volume and area of the circle, cylinder, square, cuboid, cone etc. Also draw the diagram of the figure given in the question. This helps a lot in visualizing the problem and solving it. And solve the problem in parts such as we first calculated the radius and then the volume.