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# If the volume of a right circular cone of height 9 cm is $$48 {\pi} {cm}^3$$ , find the diameter of its base.

Given :
Height (h) of cone = 9 cm
Also, Volume of cone = $$48 {\pi} {cm}^3$$

Let the radius of the cone be r.
But, Volume of cone = $$\frac{1}{3} {\pi} {r}^2 h$$
$$\Rightarrow$$ $$48 {\pi} {cm}^3$$ = $$\frac{1}{3} × {\pi} × {r}^2 × 9$$ $$cm$$
$$\Rightarrow$$$${r}^2 = \frac{48 {\pi} × 3}{9 × {\pi}} {cm}^2$$
$$\Rightarrow$$ $${r}^2 = {4}^2 {cm}^2$$
$$\Rightarrow$$ r = 4cm
$$\therefore$$ Diameter of base = 2r = 8 cm

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