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]

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. If the volume of the rectangular prism is 150 cubic inches, then we have:

150 = lwh

Since the length, width, and height are congruent in a rectangular pyramid, we can write the volume of the rectangular pyramid as:

V = (l^3)/3

Substituting l = w = h into this formula, we get:

V = (l^3)/3 = (lwh)/3

But we know that lwh = 150, so:

V = (150)/3 = 50 cubic inches

Therefore, the volume of the rectangular pyramid with congruent length, width, and height is 50 cubic inches.