Answer:
The height of the cone is 97 in
Step-by-step explanation:
Equate the formulas for the volume of a cylinder and that of a cone:
Vol-Cyl Vol-Cone
πr²h = (1/3)πr²h
Now cancel out items that are the same on both sides (π):
r²h = (1/3)r²h
Now substitute the given values for both solids:
(12 in)²(8 in) = (1/3)(6 in)²(h-cone)
1152 in³
Then (h-cone) = -------------------- = 97 in
12 in²
The height of the cone is 97 in
