Question

A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surfaces are in the ratio 8 : 5, determine the ratio of the radius of the base to the height of either of them.

A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surfaces are in the ratio 8 : 5, then find the ratio between the radius of their bases to their height.

Answer 1

Let h = height 

r = radius

`"Curved surface area of cylinder"/"Curved surface area of cone" = 8/5`

`8/5 = (2pirh)/(pirsqrt(r^2 + h^2))`

`8/5 = (2h)/sqrt(r^2 + h^2)`

`64/25 = (4h^2)/(r^2 + h^2)`   ...[squaring both sides]

64(r² + h²) = 25(4 h²)

64r² + 64h² = 100h²

64r² = 100h² − 64h²

64r² = 36h²

16r² = 9h²

`r^2/h^2 = 9/16`

`r/h = 3/4`

∴ r : h = 3 : 4