Question

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

• A. $8cm$
• B. $5cm$
• C. $3cm$
• D. $2cm$

Answer 1

Answer: (A)

Let radius of base of cone$=rcm$.
Given, height of cone$=9cm$
and volume of cone$=48\pi {cm}^3$.

$⟹$ $\frac{1}{3}\pi r^{2}h=48\pi$

$⟹$$\frac{1}{3}\times r^2\times 9=48$

$⟹$$r^2=\frac{48\times 3}{9}=16$

$⟹$$r=\sqrt{16}=4cm$.

$\therefore$ Diameter of base $=2r=2\times 4=8cm$.

Hence, option $A$ is correct.