Frustum of a Right Circular Cylinder

If $r$ is the radius and $h$ is the height of the frustum, then:

(i)  The volume of the frustum of the circular cylinder
${\text{ = }}\,{\text{Area}}\,{\text{of}}\,{\text{the}}\,{\text{base}} \times \,{\text{average}}\;{\text{height, }}{h_a}$

i.e. $V = \pi {r^2}{h_a}$

(ii) The curved surface area of the frustum
$= 2\pi r{h_a}$

(iii) The total surface area = curved surface area + area of the ends
$= 2\pi r{h_a} + \pi {r^2} + \pi ab$

Example:

A circular cylinder having a radius of 2.3m is cut in the shape of a frustum with ${h_a} = 57{\text{m}}$. Find the volume and the lateral surface area.

Solution:
(a) $V = \pi {r^2}{h_a} = \pi {\left( {2.3} \right)^2}\left( {5.7} \right)\,\,\,\,\, = 94.73\,{\text{cu}}{\text{. m}}$

(b) Curved surface area
$= 2\pi r{h_a} = 2\pi \left( {2.3} \right)\left( {5.7} \right)$
$= 82.37\,{\text{sq}}{\text{.}}\,{\text{m}}$