Question

The largest sphere is carved out of a cube of side $10.5cm$. Find the volume of the sphere.

Answer 1

Given: Side of cube $=10.5cm$

$\therefore$ Diameter of the largest sphere which can be carved out of a cube $=$ Side of cube $=10.5cm$

$\therefore$ Radius of the sphere $r=\frac{10.5}{2}cm=5.25cm$

Volume of the sphere $=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\times \frac{22}{7}\times (5.25{)}^3$

$=\frac{4}{3}\times \frac{22}{7}\times 5.25\times 5.25\times 5.25$

$=4\times 22\times 1.75\times 0.75\times 5.25$

$=606.375c{m}^3$

Hence, volume of the sphere is $606.375c{m}^3$.