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

Given,

Height of the cone (h) = 9 cm

Let radius of base of cone be r cm.

Volume of cone = 48π cm³

Substituting values we get :

$\Rightarrow \dfrac{1}{3}πr^2h = 48π \\[1em] \Rightarrow r^2 = \dfrac{48π \times 3}{πh} \\[1em] \Rightarrow r^2 = 48 \times \dfrac{3}{h} \\[1em] \Rightarrow r^2 = 48 \times \dfrac{3}{9} \\[1em] \Rightarrow r^2 = \dfrac{144}{9} \\[1em] \Rightarrow r^2 = 16 \\[1em] \Rightarrow r = \sqrt{16} \\[1em] \Rightarrow r = 4 \text{ cm}.$

By formula,

Diameter = 2 × radius = 2 × 4 cm = 8 cm.

Hence, the diameter of base of cone is 8 cm.