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A cone of height 12 cm is cut by two planes parallel to its base, at 4 cm and 8 cm from the apex. Find the ratio of the volumes of the three pieces formed, in order top : middle : bottom.

1. 1:7:19
2. 1:8:27
3. 8:19:37
4. 1:26:64

Correct answer: 1:7:19

Solution

The cones of heights 4, 8 and 12 have volumes in the ratio 1 : 8 : 27 (cubes of 1:2:3). The slices are top = 1, middle = 8-1 = 7, bottom = 27-8 = 19, giving 1 : 7 : 19.

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