2022 · Q81
The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is (1)/(27) of the volume of the given cone, then what is the height of the frustum of the cone?
Elementary MathematicsMensuration
- A10 cm
- B12 cm
- C18 cm
- D20 cm
Explanation
Volume ratio 1/27 implies linear ratio 1/3, so the cut-off cone has height 30/3 = 10 cm; the frustum height is 30−10 = 20 cm. Volumes scale as the cube of the linear scale, so a 1/27 volume ratio means a 1/3 linear ratio. The keyed option is D.