Question

A sphere and a hemisphere have same total surface area. Find the ratio of their radii i.e.$\frac{r_1}{r_2}$, where $r_1$ and $r_2$ are the radii of sphere and hemisphere respectively.

• A. 1
• B. $\frac{3}{2}$
• C. $\frac{\sqrt{3}}{4}$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is D

$\frac{\sqrt{3}}{2}$

Total surface area of a sphere is
$=4\pi {r_1}^2$

Total surface area of a hemisphere
$=3\pi {r_2}^2$

Since both are equal,
$4\pi$${r_1}^2$ = 3$\pi$${r_2}^2$

$\Rightarrow$ $\frac{{r_1}^2}{{r_2}^2}$ = $\frac{3}{4}$

$\Rightarrow$ $\frac{r_1}{r_2}$ = $\frac{\sqrt{3}}{2}$​