Respuesta :
Given:
The volume of a cylinder is [tex]30 \pi[/tex] cubic units.
A cone shares the same base.
The height of the cone is twice the height of the cylinder.
We need to determine the volume of the cone.
Height of the Cone:
Let h denote the height of the cylinder.
Let H denote the height of the cone.
Since, it is given that, the height of the cone is twice the height of the cylinder, we have;
[tex]H=2h[/tex]
Volume of the cylinder:
The formula to determine the volume of the cylinder is
[tex]V=\pi r^2 h[/tex]
Since, volume of the cylinder is [tex]30 \pi[/tex], we get;
[tex]30 \pi = \pi r^2 h[/tex] -------(1)
Volume of the cone:
The formula to determine the volume of the cone is
[tex]V=\frac{1}{3} \pi r^2 H[/tex]
Substituting [tex]H=2h[/tex], we get;
[tex]V=\frac{1}{3} \pi r^2 (2h)[/tex]
[tex]V=\frac{2}{3} \pi r^2 h[/tex]
Substituting equation (1), we get;
[tex]V=\frac{2}{3} (30 \pi)[/tex]
[tex]V=20 \pi[/tex]
Thus, the volume of the cone is 20π
Hence, Option C is the correct answer.
