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?

Side of cube = a
Volume of cube = $$a^3$$
For the maximum volume,
Height of right circular cylinder = a
Diameter = a
Radius = a/2
Volume of right circular cylinder = $$\pi r^2 h = \frac{22}{7} \times (\frac{a}{2})^2 \times a = \frac{11}{14}a^3$$
=$$0.78a^3$$
Material left = $$a^3 - 0.7857a^3 = 0.2143a^3$$
Percentage material left = $$\frac{0.2143a^3}{a^3} \times 100$$ = $$21.43 \approx 21$$%
$$\therefore$$ The correct answer is option D.