2025 · Q78
A cone and a hemisphere have equal base and equal volume. What is the ratio of the cone's height to the hemisphere's radius?
Elementary MathematicsMensuration
- A1:1
- B1:2
- C2:1
- D3:1
Explanation
Cone volume (1/3)pi*r^2*h equals hemisphere volume (2/3)pi*r^3. Cancelling (1/3)pi*r^2 gives h = 2r, so the height-to-radius ratio is 2:1. Mixing up the hemisphere volume with the full sphere's 4/3 pi r^3 is the trap.