A cone of height 15 cm and base diameter 30 cm is carved out of a wooden sphere of radius 15 cm. The percentage of wood wasted is :

Answer: Option D

Volume of sphere :
$$=\left(\frac{4}{3}\pi \times 15\times 15\times 15\right)c{m}^3$$
Volume of cone :
$$=\left(\frac{1}{3}\pi \times 15\times 15\times 15\right)c{m}^3$$
Volume of wood wasted :
$$\begin{array}{rl}& =\left[\left(\frac{4}{3}\pi \times 15\times 15\times 15\right)-\left(\frac{1}{3}\pi \times 15\times 15\times 15\right)\right]\\ & =\left(\pi \times 15\times 15\times 15\right)\end{array}$$
∴ Required percentage :
$$\begin{array}{rl}& =\left(\frac{\pi \times 15\times 15\times 15}{\frac{4}{3}\pi \times 15\times 15\times 15}\right)\%\\ & =75\%\end{array}$$