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 :

Solution (By Examveda Team)

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 :
$$\eqalign{ & = \left[ {\left( {\frac{4}{3}\pi \times 15 \times 15 \times 15} \right) - \left( {\frac{1}{3}\pi \times 15 \times 15 \times 15} \right)} \right] \cr & = \left( {\pi \times 15 \times 15 \times 15} \right) \cr} $$
∴ Required percentage :
$$\eqalign{ & = \left( {\frac{{\pi \times 15 \times 15 \times 15}}{{\frac{4}{3}\pi \times 15 \times 15 \times 15}}} \right)\% \cr & = 75\% \cr} $$