Question

If the ratio of volume to total surface area of a solid sphere is 8:1, then the radius of the sphere is units.

• A. 24
• B. 8
• C. 16
• D. 20

Answer 1

The correct option is A 24

Consider a sphere of radius r units.

We know:
$\text{Volume of a sphere}=\frac{4}{3}\pi r^3$


$\text{Total surface area of a sphere}=4\pi r^2$
Given, ratio of volume to total surface area of the sphere is 8:1.

On putting the values, we get:
$\frac{\frac{4}{3}\pi r^3}{4\pi r^2}=\frac{8}{1}$

$\frac{\text{/}4\text{/}\pi {}^r\text{/}{r}^3}{3\times \text{/}4\text{/}\pi \text{/}{r}^2}=\frac{8}{1}$

$\Rightarrow \frac{r}{3}=8$
$\Rightarrow r=24\text{units}$

Hence, the radius of the given sphere is 24 units.