The largest possible sphere is cut out from a wooden solid cube of 7 𝑐𝑚. Find the volume of the wooden left. $\left[\text{ use }\pi =\frac{22}{7}\right]$

It is given that 

Diameter of the wooden solid=side of the cube = 7𝑐𝑚

Radius of the wooden solid = 3. 5 𝑐m

$\begin{array}{r}\text{ Volume of the cube }=(\text{ side }{)}^3\\ \text{ Volume of the cube }=(7{)}^3\\ \text{ Volume of the sphere shaped wood }=\frac{4}{3}\times \pi r^3\\ =\frac{4}{3}\times \pi \times (3.5{)}^3\end{array}$

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

$\begin{array}{r}=(7{)}^3-\left(\frac{4}{3}\times \pi \times (3.5{)}^3\right)\\ =(7{)}^3-\left(\frac{4}{3}\times \frac{22}{7}\times \left(\frac{7}{2}\times \frac{7}{2}\times \frac{7}{2}\right)\right)\\ =343-\frac{49\times 11}{3}\\ =343-179.67\\ =163.33{\mathrm{cm}}^3\end{array}$