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Two right prisms each stand 12 cm tall. One has a base that is an equilateral triangle of side 8 cm, the other a square base of side 8 cm. Find the ratio of the volume of the triangular prism to that of the square prism.

1. √3 : 4
2. 3√3 : 4
3. 4 : √3
4. 3 : 4√3

Correct answer: √3 : 4

Solution

With equal heights, the volume ratio equals the base-area ratio. The triangle's area is (√3/4)(8²) and the square's is 8², giving a ratio of (√3/4) : 1 = √3 : 4.

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