A solid cone of height 9 cm with diameter of its base 18 cm is cut out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is:

Solution (By Examveda Team)

$$\eqalign{ & {\text{Volume of sphere}} = \frac{4}{3}\pi {r^3} \cr & = \frac{4}{3}\pi {\left( 9 \right)^3} \cr & = 972\pi {\text{ c}}{{\text{m}}^3} \cr & {\text{Volume of cone}} = \frac{1}{3}\pi {r^2}h \cr & = \frac{1}{3}\pi {\left( 9 \right)^2}9 \cr & = 243\pi {\text{ c}}{{\text{m}}^3} \cr & \Rightarrow \% {\text{ of wasted wood}} \cr & = \frac{{\left( {972 - 243} \right)\pi }}{{972\pi }} \times 100 \cr & = 75\% \cr} $$