The surface areas of two spheres are in the ratio 1:4. Find the ratio

1.	The surface areas of two spheres are in the ratio 1:4. Find the ratio of their volumes.
Answer» Consider r and R as the radii of two spheres We know that 4πr²/ 4πR² = ¼ So we get (r/ R)² = (1/ 2)² It can be written as r/ R = ½ Consider V₁ and V₂ as the volumes of the spheres So we get V₁/ V₂ = (4/3 πr³)/ (4/3 πR³) We can write it as (r/ R)³ = (1/ 2)³ = 1/8 Therefore, the ratio of their volumes is 1: 8.

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

Answer»

Consider r and R as the radii of two spheres

We know that

4πr²/ 4πR² = ¼

So we get

(r/ R)² = (1/ 2)²

It can be written as

r/ R = ½

Consider V₁ and V₂ as the volumes of the spheres

So we get

V₁/ V₂ = (4/3 πr³)/ (4/3 πR³)

We can write it as

(r/ R)³ = (1/ 2)³ = 1/8

Therefore, the ratio of their volumes is 1: 8.