Question

The curved surface area of a cylinder is 198cm² and its base has diameter 21cm. Find the height and the volume of the cylinder.

Answer 1

The curved surface area of a cylinder = 198cm²
Diameter of base = 21cm
∴ Radius (r) = 10.5cm
Let h be the height of the cylinder
L.S.A. = 198cm²
2 x π x r x h = 198     ...[∵ L.S.A of cylinder = 2 x π x r x h]

`2 xx (22)/(7) xx 10.5 xx "h"` = 198

`(462)/(7)"h"` = 198

h = `(198 xx 7)/(462)`

h = `(1386)/(462)` = 3cm
Volume of cylinder
= π x r² x h

= `(22)/(7) xx 10.5^2 xx 3`
= 1039.5cm³.