What is the ratio of the volume

Solution:

Ratio of sphere

$=\frac{1}{2} \times$ side of cube

$r=\frac{a}{2}$

Now,

Volume of cube $v_{1}=a^{3}$

 

Volume of sphere

$v_{2}=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \pi\left(\frac{a}{2}\right)^{3}$

$=\frac{4}{3} \pi \frac{a^{3}}{8}$

$v_{2}=\frac{1}{6} \pi a^{3}$

The ratio of their volumes

$v_{1}: v_{2}=a^{3}: \frac{1}{6} \pi a^{3}$

$\frac{v_{1}}{v_{2}}=\frac{a^{3}}{\frac{1}{6} \pi a^{3}}$

$=\frac{6}{\pi}$

Hence, $v_{1}: v_{2}=6: \pi$