A toy is in the form of a cone mounted on a hemisphere of the same radius 3.5 cm. The total height of the toy is 15.5 cm. Find the volume of the toy. \(\left(\pi = \dfrac{22}{7}\right)\)

Answer: About 243.83 cm\(^3\)

[Figure: A cone standing on the flat face of a hemisphere; common radius 3.5 cm; total height 15.5 cm.]

Height of cone h = 15.5 – 3.5 = 12 cm (the hemisphere’s height is its radius).

\(\pi r^2 = \dfrac{22}{7} \times 3.5 \times 3.5 = 38.5\)

Volume of cone \(= \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 38.5 \times 12 = 154\) cm\(^3\).

Volume of hemisphere \(= \dfrac{2}{3}\pi r^3 = \dfrac{2}{3} \times 38.5 \times 3.5 = \dfrac{269.5}{3} \approx 89.83\) cm\(^3\).

Volume of toy = 154 + 89.83 = 243.83 cm\(^3\).