2018 · Q69
A right circular cone is sliced into a smaller cone and a frustum of a cone by a plane perpendicular to its axis. The volume of the smaller cone and the frustum of the cone are in the ratio 64:61. Then their curved surface areas are in the ratio
Elementary MathematicsMensuration
- A4:1
- B16:9
- C64:61
- D81:64
Explanation
Volume ratio 64 : 61 for small cone : frustum means small : whole = 64 : 125, so the linear scale ratio is ∛(64/125) = 4 : 5. Curved surface areas scale as squares: 16 : 25, so the frustum's share is 25 − 16 = 9 units and small : frustum = 16 : 9, option (B).