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A prism stands on a rectangular base whose length equals three times its breadth, and the base perimeter is 40 cm. The prism is built in three layers whose heights fall in an arithmetic progression: 20 cm for the lowest layer down to 12 cm for the third layer. Find the prism's total volume.

1. 3200 cm^3
2. 4000 cm^3
3. 4500 cm^3
4. 3600 cm^3

Correct answer: 3600 cm^3

Solution

From 8w = 40, w = 5 cm and length = 15 cm, so base area = 75 cm^2. The layer heights 20, 16, 12 (AP with middle term 16) total 48 cm, giving volume 75 x 48 = 3600 cm^3.

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