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 the toy.

Given,

The solid wooden toy is in the shape of a right circular cone mounted on a hemisphere.

Radius of hemisphere (r) = 4.2 cm

Total height (h) = 10.2 cm.

Height of conical part (h₁) = 10.2 - 4.2 = 6 cm.

Volume of toy (V) = Volume of cone + Volume of hemisphere

= $\dfrac{1}{3}πr^2h + \dfrac{2}{3}πr^3$

Putting values we get,

$V = \dfrac{1}{3}πr^2\Big(h + 2r\Big) \\[1em] = \dfrac{1}{3} \times \dfrac{22}{7} \times (4.2)^2 \times (6 + 2(4.2)) \\[1em] = \dfrac{22 \times 17.64 \times 14.4}{21} \\[1em] = \dfrac{5588.352}{21} \\[1em] = 266.112 \text{ cm}^3.$

Hence, the volume of the toy = 266.112 cm³.