Question

If the volume of a sphere is equal to the volume of the hemisphere, then find the ratio of the radius of the sphere to the radius of the hemisphere.

• A. $2:\sqrt[3]{32}$
• B. $1:\sqrt[3]{32}$
• C. $1:\sqrt[3]{33}$
• D. $1:\sqrt[3]{37}$

Answer 1

The correct option is B $1:\sqrt[3]{32}$

Let the radius of the sphere be $r_1$ and the radius of the hemisphere be $r_2$.
Then,
Volume of sphere, $V_1=\frac{4}{3}\pi (r_1{)}^3$

Volume of hemisphere, $V_2=\frac{2}{3}\pi (r_2{)}^3$

Given, volume of sphere is equal to the volume of hemisphere.
$\frac{4}{3}\pi (r_1{)}^3=\frac{2}{3}\pi (r_2{)}^3$
$\frac{r_1}{r_2}=\frac{1}{\sqrt[3]{32}}$
$\therefore r_1:r_2=1:\sqrt[3]{32}$