Question

From a solid cylinder whose height is 15 cm and the diameter is 16 cm, a conical cavity of the same height and same diameter is hollowed out, Find the total surface area of remaining solid. (Give your answer in terms of π).

Answer 1

Height of cylinder, h = 15 cm

Diameter of cylinder = 16 cm

∴ Radius of cylinder, r = `16/2` = 8 cm

Let slant height of cone be l cm

∴ `l = sqrt(r^2 + h^2)  cm`

= `sqrt(8^2 + 15^2)`

= `sqrt(64 + 225)`

= `sqrt(289)`

∴ l = 17 cm

T.S.A. of reaming solid = Top area of cylinder + C.S.A. of cylinder + C.S.A. of conical Vanity

= πr² + 2πrh + πrl

= πr(r + 2h + l)

= π × 8(3 + 2 × 15 + 17)

= π × 8 × 55

T.S.A. of reaming solid = 440π cm².