A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the ratio between radius of their bases to their height is 3 : 4.

### Answer

Let r be the radii of bases of cylinder and cone and h be the height

Slant height of cone = √(r^{2} + h^{2})

∴ 2πrh / πr√(r^{2} + h^{2}) = 8/5

h / √(r^{2} + h^{2}) = 4/5

h^{2} / (r^{2} + h^{2}) = 16/25

⇒ 25h^{2} = 16r^{2} + 16h^{2}

⇒ 9h^{2} = 16r^{2}

⇒ r^{2} / h^{2} = 9/16

r / h = 3/4