Frustum of a Right Circular Cylinder

If r is the radius and h is the height of the frustum, then
(i)         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}


frustum-cylinder

(ii)        Curved surface area of the frustum
                         = 2\pi r{h_a}
(iii)       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 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}}

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