Question

The diameter of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surface areas.

Answer 1

Let radius of each cone = r

Ratio between their slant heights = 5:4

Let slant height of the first cone = 5x

and slant height of second cone = 4x

Therefore, curved surface area of the first cone =

πrℓ = πr × (5x) = 5πrx

curved surface area of the second cone = πrℓ = πr × (4x) = 4πrx

Hence, ratio between them = 5πrx : 4πrx = 5 : 4