Question

The ratio of the radii of 2 spheres is $2:3$. Find the ratio of their volumes.

• A. $4:9$
• B. $8:27$
• C. $2:3$
• D. $1:1$

Answer 1

The correct option is B $8:27$

Volume of a sphere $=\frac{4}{3}\pi r^2$
Let $r_1$ and $r_2$ be the radii of the 2 spheres, and let $V_1$ and $V_2$ be the volumes of the 2 spheres.
So, let $r_1=2x$ and $r_2=3x$
So, $\frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3}$
$=\frac{(2x{)}^3}{(3x{)}^3}=\frac{8}{27}$