If the volume of a right circular cone of height $ 9 \mathrm{~cm} $ is $ 48 \pi \mathrm{cm}^{3} $, find the diameter of its base.
Given:
The volume of a right circular cone of height $9\ cm$ is $48 \pi\ cm^3$.
To do:
We have to find the diameter of its base.
Solution:
Height of the cone $h = 9\ cm$
Volume of the right circular cone $=48 \pi cm^{3}$
This implies,
$\frac{1}{3} \pi r^{2} h =48 \pi$
$\frac{1}{3} \pi r^{2} \times 9 = 48 \pi$
$r^{2} = \frac{48}{3}$
$r^2= 16$
$r=\sqrt{16}$
$r= 4\ cm$
This implies,
Diameter of the base $=2r$
$=2\times4$
$=8\ cm$
Hence, the diameter of the right circular cone is $8\ cm$.
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