MathematicsThe ratio of the volumes of two spheres is 8:27. Then, which of the following is the ratio of their radii?

The ratio of the volumes of two spheres is $8 : 27$ . Then, which of the following is the ratio of their radii?

Given,
Ratio of volume of spheres

= 8 : 27

.
Volume of sphere

= \frac{4}{3} π r^{3}

. Let

R

be the radius of one sphere and

r

be the radius of another sphere.

Ratio = \frac{\frac{4}{3} π R^{3}}{\frac{4}{3} π r^{3}}

Ratio = 8 : 27

∴ \frac{R^{3}}{r^{3}}

= 8 : 27

∴ \frac{R}{r} = 2 : 3

Hence, the ratio of radius is

2 : 3

.
Therefore, option 2 is correct.

JEE