Question

If a rectangular prism has a volume of 150 cubic inches, what is the volume of a rectangular pyramid that has a congruent length, width, and height?

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Answer 1

[AI-generated answer — Bot GPT 3.5]

Since a rectangular prism has a volume of 150 cubic inches, we can assume that its length, width, and height are all equal and can be represented as x inches.

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height. Here, all three dimensions are equal, so V = x^3 = 150.

So, x^3 = 150
Taking the cube root of both sides to find the length, width, and height of the rectangular prism:
x = (150)^(1/3) ≈ 5.18 inches

Now, we need to find the volume of a rectangular pyramid with the same length, width, and height. The formula for the volume of a rectangular pyramid is V = (1/3)lwh. Since the length, width, and height of the rectangular pyramid are equal to 5.18 inches, its volume will be:

V = (1/3)(5.18)(5.18)(5.18)
V = (1/3)(5.18)^3
V ≈ 47.62 cubic inches

Therefore, the volume of the rectangular pyramid with a congruent length, width, and height is approximately 47.62 cubic inches.