Question

A rectangular pyramid has the volume of 480 in ^3. If the base and height are congruent, what is the volume of the pyramid

Answer 1

[AI-generated answer — Bot GPT 3.5]

The volume of a rectangular pyramid is given by the formula V = (1/3) * base area * height.

If the base and height are congruent, the base area can be represented as x^2, where x is the length of a side of the base.

Given that the volume of the pyramid is 480 in^3, we have:

480 = (1/3) * x^2 * x

480 = (1/3) * x^3

Multiplying both sides by 3:

1440 = x^3

Taking the cube root of both sides:

x = 12

So, the length of a side of the base is 12 in.

The volume of the pyramid is:

V = (1/3) * 12^2 * 12
V = (1/3) * 144 * 12
V = 576 in^3

Therefore, the volume of the pyramid is 576 in^3.