A right circular cylinder of maximum volume is cut out from a solid wooden cube. The material left is what percent of the volume (nearest to an integer) of the original cube?

Solution (By Examveda Team)

$$\eqalign{ & {V_1}{\text{ of cube}} = {a^3} \cr & {V_2}{\text{ of cylinder}} = \pi {\left( {\frac{a}{2}} \right)^2} \times a \cr & {V_1}:{V_2} = {a^3}:\frac{{22}}{7} \times \frac{{{a^3}}}{4} = 14:11 \cr & {\text{Remaining part}}:{V_1} = 3:14 \cr & \% = \frac{3}{{14}} \times 100 = \frac{{150}}{7} = 21\% \cr} $$