A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm. Find the volume of wooden toy (nearly)?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Height of the cone}} = 10.2 - 4.2 = 6{\text{ cm}} \cr & {\text{Volume of the toy}} = \frac{1}{3}\pi {r^2}h + \frac{2}{3}\pi {r^3} \cr & = \frac{1}{3}\pi {r^2}\left( {h + 2r} \right) \cr & = \frac{1}{3} \times \frac{{22}}{7} \times {\left( {4.2} \right)^2}\left( {2 \times 4.2 + 6} \right) \cr & = \frac{1}{3} \times \frac{{22}}{7} \times {\left( {4.2} \right)^2} \times 14.4 \cr & = 266{\text{ c}}{{\text{m}}^3}{\text{ }}\left( {{\text{appx}}{\text{.}}} \right) \cr} $$