Question

The radii of two solid spheres are 10 cm and 20 cm. The ratio between their volumes is:

Options

• 3 : 8

• 1 : 4

• 1 : 8

• 8 : 3

Answer 1

1 : 8

Explanation:

Radius of first solid sphere (r) = 10 cm

Radius of second solid sphere (R) = 20 cm

Ratio of volumes of two spheres:

\[\Rightarrow \frac{\text{Vol. of 1st sphere}}{\text{Vol. of 2nd sphere}} = \frac{\frac{4}{3}\, \pi r^3}{\frac{4}{3}\, \pi R^3}\]

\[{} = \frac{r^3}{R^3}\]

\[{} = \frac{10^3}{20^3}\]

\[{} = \frac{1000}{8000}\]

\[{} = \frac{1}{8}\]

= 1 : 8