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A right circular cone of height 40 cm is sliced by two planes parallel to its base, located 10 cm and 20 cm below the apex. In what ratio (apex part : middle part : bottom part) do the volumes of the three resulting pieces stand?

1. 1 : 7 : 56
2. 1 : 8 : 64
3. 1 : 7 : 19
4. 1 : 8 : 27

Correct answer: 1 : 7 : 56

Solution

Cones formed from the apex are similar, so their volumes are proportional to the cube of the height from the apex: 1 : 8 : 64. Subtracting successive cumulative volumes gives slices 1, 7, 56, i.e. 1 : 7 : 56.

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