Question

The surface areas of two spheres are in the ratio 1:4. find the ratio of their volumes.

Answer 1

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Answer 2

We know area of a sphere is given by

A = 4 * 3.14 * (radius)^2

And

Volume = (4/3) * 3.14 * (radius)^3

Let the radii of two spheres be r and R respectively.

Ratio of their surface areas is

(4*3.14*r^2)/(4*3.14*R^2) = 1/4

Or (r/R)^2 = (1/2)^2

Or r/R = 1/2

Now the ratio of their volumes is

((4/3)*3.14*r^3)/((4/3)*3.14*R^3)

= (r/R)^3

= (1/2)^3

= 1/8

So the ratio of their volumes is 1:8

This is your answer.