If the volume of a right circular cone of height 9 cm is 48π cm³, find the diameter of its base.

We know,

Volume of cone = $\dfrac{1}{3}πr^2h$.

Given, Volume of cone = 48π cm³ and h = 9 cm.

$\Rightarrow \dfrac{1}{3}πr^2h = 48π \\[1em] \Rightarrow r^2 = \dfrac{48π \times 3}{π \times h} \\[1em] \Rightarrow r^2 = \dfrac{48π \times 3}{π \times 9} \\[1em] \Rightarrow r^2 = 16 \\[1em] \Rightarrow r = \sqrt{16} = 4 \text{ cm}.$

Diameter = 2 × Radius = 2 × 4 = 8 cm.

Hence, the diameter of the base = 8 cm.