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

Answer 2

Let their slant height be 5x and 4x.

Given that diameter of two cones are equal

∴ R₁ = R₂ = R

S₁ = πRl = πR(5x)

S₂ = πRl = πR(4x)

`(S_1)/(S_2) = (πR (5x))/(πR (4x)) = 5/4`

`(S_1)/(S_2) = 5/4`

S₁ : S₂ = 5 : 4.