Question

The total surface area of a cylinder is 3872cm². Find its height and volume if the circumference of the base is 88cm.

Answer 1

T.S.A. of cylinder = 3872cm²
Let r and h be the radius and height of the cylinder respectively.
Circumference of the base = 88cm
i.e., 2 x π x r = 88

`2 xx (22)/(7) xx "r"` = 88

r = `(88 xx 7)/(44)`
= 14cm
T.S.A. of cylinder = 3872cm²
(2 x π x r x h) + (2 x π x r²) = 3872

`(2 xx (22)/(7) xx 14 xx "h") + (2 xx (22)/(7) xx 14^2)` = 3872
88h + 1232 = 3872
88h = 2640

h = `(2640)/(88)`
h = 30cm
Thus,
Volume of cylinder
= π  x r² x h

= `(22)/(7) xx 14^2 xx 30`
= 18480cm³.