A solid is in the form of a cone standing on a hemisphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find in terms of π, the volume of the solid.

Given,

Radius of both cone and hemisphere (r) = 8 cm

Height of cone (h) = 8 cm

From figure,

Volume of the solid = Volume of cone + Volume of hemisphere

$= \dfrac{1}{3}πr^2h + \dfrac{2}{3} πr^3 \\[1em] = \dfrac{1}{3} \times π \times 8^2 \times 8 + \dfrac{2}{3} \times π \times 8^3 \\[1em] = \dfrac{1}{3}.π.8^3 + \dfrac{2}{3}.π.8^3 \\[1em] = \Big(\dfrac{1 + 2}{3}\Big) \times π \times 512 \\[1em] = 512π \text{ cm}^3.$

Hence, volume of solid = 512π cm³.