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?

Answer: Option A

Solution

Answer: Option A

Solution:

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