2024 · Q87
A cone, a hemisphere and a cylinder stand on equal base of radius r and have the same height. If the sum of volumes of cone, the hemisphere and the cylinder is equal to volume of a sphere of radius R, then what is R³r³ equal to?
Elementary MathematicsMensuration
- A1.25
- B1.5
- C2
- D2.5
Explanation
The three solids share base radius r and height r. Their volumes: cone πr³/3, hemisphere 2πr³/3, cylinder πr³, summing to 2πr³. Setting this equal to the sphere's volume (4/3)πR³ gives 2r³ = (4/3)R³. Thus R³/r³ = 3/2 = 1.5 — option B.