Question

The largest possible sphere is carved out of a wooden solid cube of side 7 cm. Find the volume of the wood left. $[Use\pi =\frac{22}{7}]$

Answer 1

Diameter of Sphere = Side of cube = 7 cm
Hence, radius of sphere = $\frac{7}{2}$ cm
Volume of wood left = Volume of cube - volume of sphere
= $s^3-\frac{4}{3}\pi r^3$
= $7\times 7\times 7-\frac{4}{3}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{7}{2}$
= $343-\frac{539}{3}$
= $\frac{490}{3}$
= $163.33c{m}^3$