Answer: [tex]8\ in.[/tex]
Step-by-step explanation:
Given
Radius and height of cylinder is 8 and 6 inches
Similarly the radius of cone is 12 inches
If they have same volume
Equate the volume of cylinder and cone
[tex]\Rightarrow \pi r^2h=\dfrac{1}{3}\pi r'^2h'\\\\\Rightarrow \pi \cdot 8^2\times 6=\dfrac{1}{3}\pi \cdot 12^2\times h\\\\\Rightarrow h=\dfrac{64\times 18}{144}\\\\\Rightarrow h=8\ in.[/tex]
Therefore , the height of cone is 8 in.
