Question

The ratio of the volumes of two spheres is $8:27$. The ratio of their radii is

• A. $3:2$
• B. $2:3$
• C. $4:3$
• D. $2:9$

Answer 1

Answer: (B)

$2:3$

Given, ratio of volume of spheres $=8:27$
Volume of sphere $=\frac{4}{3}\pi r^3$
Let $R$ be the radius of one sphere and $r$ be the radius of another sphere.
$\therefore$ Ratio $=\frac{\frac{4}{3}\pi R^3}{\frac{4}{3}\pi r^3}$ $=8:27$
$\therefore \frac{R^3}{r^3}$ $=8:27$
$\therefore \frac{R}{r}=2:3$