A rectangular prism has a volume of 252 in.3 . If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?(1 point)
in.3
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The volume of a rectangular pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.
Since the base and height of the pyramid are congruent to the prism, the base of the pyramid will have the same dimensions as the base of the prism. Therefore, the base area of the pyramid will be the same as the base area of the prism.
Given that the volume of the prism is 252 in^3, we can find the dimensions of the base of the prism by taking the cube root of 252:
252^(1/3) ≈ 6.83 in
Therefore, the base area of the pyramid will be (6.83 in)^2 = 46.6 in^2.
Since the height of the pyramid is also congruent to the height of the prism, we can find the height of the pyramid by dividing the volume of the prism by the base area of the pyramid:
252 in^3 / 46.6 in^2 ≈ 5.41 in
Now that we have the base area and the height of the pyramid, we can calculate the volume of the pyramid:
V = (1/3) * 46.6 in^2 * 5.41 in ≈ 84.2 in^3
Therefore, the volume of the pyramid is approximately 84.2 in^3.