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A column is shaped like a regular triangular prism whose base edge measures 8 cm. It is constructed in three stacked segments whose heights are 10 cm, 12 cm and 14 cm. Find the total volume of the column.

1. 576 sqrt(3) cm^3
2. 288 sqrt(3) cm^3
3. 144 sqrt(3) cm^3
4. 432 sqrt(3) cm^3

Correct answer: 576 sqrt(3) cm^3

Solution

The base area is (sqrt(3)/4) x 8^2 = 16 sqrt(3) cm^2. The three stacked segments give a combined height of 10 + 12 + 14 = 36 cm, so the volume is 16 sqrt(3) x 36 = 576 sqrt(3) cm^3.

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