Question

The circumference of the base of a cylinder is 132 cm and its height is 25 cm. Find the volume of the cylinder.

Answer 1

Hint- Here, we will proceed by using the formula for the circumference of the base of the cylinder which is given by $2\pi r$ and from here we will find the radius of the cylinder. Then, we will apply the formula i.e., Volume of the cylinder = $\pi {r^2}h$.

Complete Step-by-Step solution:
Let us consider a cylinder having the radius of the base as r cm as shown in the figure
Given, Height of the cylinder, h = 25 cm
Circumference of the base of the cylinder = 132 cm
As we know that the circumference of the base of any cylinder having radius r and height h is given by
Circumference of the base of the cylinder = $2\pi r$
$ \Rightarrow 132 = 2\pi r$
Taking $\pi = \dfrac{{22}}{7}$, we have
$
   \Rightarrow 132 = 2\left( {\dfrac{{22}}{7}} \right)r \\
   \Rightarrow r = \dfrac{{132}}{{2\left( {\dfrac{{22}}{7}} \right)}} \\
   \Rightarrow r = \dfrac{{132 \times 7}}{{44}} = 3 \times 7 \\
   \Rightarrow r = 21{\text{ cm}} \\
 $
The radius of the given cylinder is 21 cm
Also, we know that the volume of any cylinder having radius r and height h is given by
Volume of the cylinder = $\pi {r^2}h$
Using the above formula, the required volume of the given cylinder is given by
${\text{V}} = \pi {r^2}h$
Putting r = 21 cm, h = 25 cm and $\pi = \dfrac{{22}}{7}$ in the above equation, we have
$
   \Rightarrow {\text{V}} = \left( {\dfrac{{22}}{7}} \right) \times {\left( {21} \right)^2} \times 25 \\
   \Rightarrow {\text{V}} = 34650{\text{ c}}{{\text{m}}^3} \\
 $
Therefore, the required volume of the given cylinder is 34650 ${\text{c}}{{\text{m}}^3}$.

Note- The radius of any cylinder always remains constant i.e., the radius is the same at any level as the radius at the base. Since, the base of any cylinder is circular in geometry (having radius of the circle as the radius of the cylinder) that’s why the circumference of the base of the cylinder is equal to the circumference of a circle having the same radius as that of the cylinder.