2021 · Q31
A cone and a hemisphere have equal bases and volumes. What is the ratio of the height of the cone to the radius of the hemisphere?
Elementary MathematicsMensuration
- A1 ∶ 1
- B2 ∶ 1
- C3 ∶ 2
- D4 ∶ 3
Explanation
Equating volumes: (1/3)πr²h = (2/3)πr³. Cancelling (1/3)πr² gives h = 2r, so the ratio of cone height to hemisphere radius is 2 : 1. Hence option B.