Question.
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.
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.
Solution:
Height (h) of cone = 9 cm
Let the radius of the cone be r.
Volume of cone $=48 \pi \mathrm{cm}^{3}$
$\Rightarrow \frac{1}{3} \pi r^{2} h=48 \pi \mathrm{cm}^{3}$
$\Rightarrow r^{2}=16 \mathrm{~cm}^{2}$
$\Rightarrow r=4 \mathrm{~cm}$
Diameter of base $=2 r=8 \mathrm{~cm}$
Height (h) of cone = 9 cm
Let the radius of the cone be r.
Volume of cone $=48 \pi \mathrm{cm}^{3}$
$\Rightarrow \frac{1}{3} \pi r^{2} h=48 \pi \mathrm{cm}^{3}$
$\Rightarrow r^{2}=16 \mathrm{~cm}^{2}$
$\Rightarrow r=4 \mathrm{~cm}$
Diameter of base $=2 r=8 \mathrm{~cm}$