Question

The ratio of volume to the total surface area of a solid sphere is 8. Find its radius.

• A. 2
• B. 2√2
• C. 24
• D. 64

Answer 1

The correct option is C

24

Volume of a sphere is given as: $\left(\frac{4}{3}\right)\times \pi \times r^3$
Total surface area of a sphere is given as: $4\pi$$r^2$
Thus, for a sphere,
$\Rightarrow$ $\frac{\text{Volume}}{\text{Surface area}}$ = $\frac{\frac{4}{3}\times \pi r^3}{4\pi r^2}$
$\Rightarrow$ $8=\frac{r}{3}$
$\Rightarrow r=24$