Given : Diameter of the right circular cone ==> 8 cm
It means : The Radius of the right circular cone is 4 cm (as Radius is half of the Diameter)
Given : Volume of the right circular cone ==> 48π cm³
We know that :
[tex]\bigstar \ \ \boxed{\textsf{Volume of a right circular cone is given by : $\pi r^2\dfrac{h}{3}$}}[/tex]
where : r is the radius of the circular cross-section.
h is the height of the right circular cone.
Substituting the respective values in the formula, we get :
[tex]\mathsf{\implies \pi \times (4)^2 \times \dfrac{h}{3} = 48\pi}[/tex]
[tex]\mathsf{\implies 16 \times \dfrac{h}{3} = 48}[/tex]
[tex]\mathsf{\implies \dfrac{h}{3} = 3}[/tex]
[tex]\implies \boxed{\mathsf{h= 9 \ cm}}[/tex]
Answer : Height of the given right circular cone is 9 cm
