Question

If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is

(a) 1 : 2

(b) 1 : 4

(c) 1 : 8

(d) 1 : 16

Answer 1

Here, we are given that the ratio of the two spheres of ratio 1:8

Let us take,

The radius of 1^st sphere = r₁

The radius of 1^st sphere = r₂

So,

Volume of 1^st sphere (V₁) =

Volume of 2^nd sphere (V₂) =

Now,

Now, let us find the surface areas of the two spheres

Surface area of 1^st sphere (S₁) =

Surface area of 2^nd sphere (S₂) =

So, Ratio of the surface areas,

Using (1), we get,

Therefore, the ratio of the spheres is. So, the correct option is (b)