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)
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.
Given that the volume of the prism is 252 in^3, we can find the dimensions of the prism by factoring 252 into its prime factors: 252 = 2^2 × 3^2 × 7.
Since the base and height of the pyramid are congruent to the prism, the dimensions of the prism would be the same as the base and height of the pyramid. Therefore, the base and height of the pyramid would be 2 in, 3 in, and 7 in.
Now, we can find the volume of the pyramid using the formula V = 1/3Bh, where B is the area of the base and h is the height.
The base area of the pyramid is A = l × w = 2 × 3 = 6 in^2.
Therefore, the volume of the pyramid would be V = 1/3 × 6 in^2 × 7 in = 14 in^3.
Therefore, the volume of the pyramid is 14 in^3.