Answer:
The correct option is C. The height of the cylinder is 9 cm.
Step-by-step explanation:
The radius of cone is 12 cm and the height of cone is 12 cm.
The volume of cone is
[tex]V=\frac{1}{3}\pi r^2h[/tex]
[tex]V_1=\frac{1}{3}\pi (12)^2(12)[/tex]
[tex]V_1=576\pi[/tex]
The radius of cylinder is 8 cm. The volume of cylinder is
[tex]V=\pi r^2h[/tex]
[tex]V_2=\pi (8)^2h[/tex]
[tex]V_2=64\pi h[/tex]
It is given that the volume of cone and cylinder is same.
[tex]V_1=V_2[/tex]
[tex]576\pi=64\pi h[/tex]
[tex]\frac{576\pi}{64\pi}=h[/tex]
[tex]9=h[/tex]
Therefore the height of the cylinder is 9 cm and option C is correct.
