Question

There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. Find the ratio of their radii. 

Answer 1

Let slant height of the first cone = l

Then slant height of the second cone = 2l

Radius of the first cone = r₁

Radius of the second cone = r₂

Then, curved surface area of first cone = πr₁l 

Curved surface area of second cone = πr₂(2l) = 2πr₂l 

According to given condition: 

πr₁l = 2(2πr₂l) 

π πr₁l = 4πr₂l 

r₁ = 4r₂ 

`r_1/r_2 = 4/1` 

∴ r₁ : r₂ = 4 : 1