Question

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

Answer 1

Given that,

Diameter of the wooden solid (Spherical in shape) $=$ Side of the cube $=7cm$

Radius of the wooden solid (Spherical in shape) $=3.5cm$

Volume of the cube = $(Side{)}^3=(7{)}^3---\left(1\right)$

Volume of sphere shaped wood = $\frac{4}{3}\times \pi r^3=\frac{4}{3}\times \pi \times {3.5}^3---\left(2\right)$

Volume of the wood left = Volume of the cube – Volume of sphere

$=7^3-(\frac{4}{3}\times \pi \times {3.5}^3)$

$=7^3-(\frac{4}{3}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{7}{2})$

$=343-\frac{49\times 11}{3}$

$=343-179.67$

$=163.33c{m}^3$