Multiple choice

A right prism has a square base with side of base 4 cm. The height of the prism is 9 cm. It is cut into three parts of equal height by two planes parallel to its base. What is the ratio of the volumes of the top, middle and bottom parts, respectively?

  1. 1 : 1 : 1

  2. 1 : 7 : 19

  3. 1 : 8 : 20

  4. 1 : 7 : 20
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A Correct answer
Explanation

The prism is cut into three parts of equal height (3 cm each). The base area is 16. Volume of top part = 16 * 3 = 48. Middle part = 16 * 3 = 48. Bottom part = 16 * 3 = 48. The ratio is 1:1:1.

AI explanation

When a right prism with a uniform cross-section is cut by planes parallel to its base, each resulting part retains the same square base of 4 cm by 4 cm. The height of each part is the total height of 9 cm divided by 3, which equals 3 cm. Since the base area and height are identical for all three parts, their volumes are equal, making the ratio 1 to 1 to 1.

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