A hemisphere and a cone share the same base and have equal volumes. Given that their common radius is R, determine the height of the cone.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 2R.
Volume of hemisphere = πR3
Volume of cone = πR2h
Given volumes are equal:
⇒ πR3 = πR2h
⇒ 2R3 = R2h
⇒ h = 2R
Height of cone = 2R