Question

A sphere and a hemisphere have the same volume. The ratio of their radii can be

• A. 1 : 8
• B. 1 : 4
• C. $1:\sqrt[3]{32}$
• D. $1:\sqrt{2}$

Answer 1

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

Let $r_1$ and $r_2$ be the radii of a sphere and a hemisphere respectively.
Since, sphere and hemisphere have the same volume.
$\therefore \frac{4}{3}\pi r_1^3=\frac{2}{3}\pi r_2^3$
$\Rightarrow 2r_1^3=r_2^3$
$\Rightarrow \frac{r_1^3}{r_2^3}=\frac{1}{2}$
$\Rightarrow \frac{r_1}{r_2}=\sqrt[3]{3\frac{1}{2}}=\frac{1}{\sqrt[3]{32}}$
$\Rightarrow r_1:r_2=1:\sqrt[3]{32}$
Hence, the correct answer is option (c).