A hemisphere, cone, and cylinder have the same base radius and equal volumes. If the height of the cylinder is h, find the height of the cone.
Show answer & explanation
Correct answer: A
Explanation
Let the base radius be r (all three are the same).
The volumes are equal:
Hemisphere = (2/3)πr³
Cylinder = πr²h
Cone = (1/3)πr²H
Now the volume of the hemisphere = the volume of the cylinder
(2/3)πr³ = πr²h
2r = 3h ...(1)
Volume of the cylinder = Volume of the cone
πr²h = (1/3)πr²H
H = 3h