Question

A tank is in the form of a right circular cylinder. Its height is 48m and the base area is 616 sq m. Find the lateral surface area and volume of the cylinder.

Answer 1

Hint:
Now, we know that the base of the cylinder is a circle. Hence, use the given area of the circle to find the radius of the cylinder. Then, substitute the values in the formula of the lateral surface of the cylinder, $2\pi rh$ and formula of the volume, which is, $\pi {r^2}h$, where $r$ is the radius of the cylinder and $h$ is the height of the cylinder.

Complete step by step solution:
We are given that height of a cylindrical tank is 48m and the base area is 616 sq m.
We know that the base area of the cylindrical is the area of the circle.
Also, the area of a circle is given by $\pi {r^2}$, where $r$ is the radius of the circle.
Substitute the values of the area and $\pi = \dfrac{{22}}{7}$ to find the radius of the cylindrical tank.
$
  616 = \dfrac{{22}}{7}{r^2} \\
   \Rightarrow {r^2} = \dfrac{{616\left( 7 \right)}}{{22}} \\
   \Rightarrow {r^2} = 196 \\
   \Rightarrow r = 14 \\
$
This implies that the radius of the cylindrical tank is 14m.
Now, we will calculate the formula of the lateral surface of the cylinder, by substituting the values in the formula, $2\pi rh$, where $r$ is the radius of the cylinder and $h$ is the height of the cylinder.
$
  A = 2\left( {\dfrac{{22}}{7}} \right)14\left( {48} \right) \\
  A = 4224{m^2} \\
$
Now, we will calculate the volume of the cylindrical tank by substituting the values in the formula, $\pi {r^2}h$
That is
$
  V = \left( {\dfrac{{22}}{7}} \right){\left( {14} \right)^2}\left( {48} \right) \\
   \Rightarrow V = 29,568{m^3} \\
$

Hence, the required answer is $29,568{m^3}$.

Note:
We can alternatively calculate volume by multiplying the area of the given base and the height of the cylinder. Volume refers to the space enclosed by an object. Volume is measured in cubic units whereas area is measured in square units.