Question

A sphere and a cube are of the same height. The ratio of their volumes is

• A. 3 : 4
• B. 21 : 11
  
• C. 4 : 3
  
• D. 11 : 21

Answer 1

The correct option is D

11 : 21

Let r be the height of a sphere and cube

$\therefore Radiusofsphere=\frac{r}{2}$

$\therefore$ Volume of sphere $=\frac{4}{3}\pi {\left(\frac{r}{2}\right)}^3$

$=\frac{4}{3}\times \frac{22}{7}\times \frac{r^3}{8}=\frac{11r^3}{21}$

and volume of cube $=r^3$

$\therefore$ Ratio between their volume

$=\frac{11r^3}{21}:r^3$

$=\frac{11}{21}:1\Rightarrow 11:21$