The surface areas of the two spheres are in the ratio 1:2. The ratio of their volumes is

Given that the surface areas of the two spheres are in the ratio= 1: 2. We know that the surface area of a sphere is

4 π r^{2}

, where

r

is the radius.
Let

r_{1}

and

r_{2}

be the radii of two spheres.
Thus, the ratio of the surface area will be:

⇒ 4 π r 12 4 π r 22 = r 12 r 22 ⇒ 12 = r 12 r 22 ⇒ r 1 r 2 = 12

Therefore, the ratio

= 1 : \sqrt{2}

.
The formula for the volume of sphere is given by,
Volume of a sphere

= 43 π r 3

, where r is the radius. So, after substituting the value of all the dimensions in the formula we get,

⇒ 43 π r 13 43 π r 23 = r 13 r 23 ⇒ 43 π r 13 43 π r 23 = 123

⇒ 43 π r 13 43 π r 23 = 122

Therefore, the ratio of their volumes is

1 : 2 \sqrt{2} .

Hence, option (3) is correct.

The surface areas of the two spheres are in the ratio $1 : 2$ . The ratio of their volumes is