There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is 48 in.3 , what is the volume of the prism?(1 point) Responses 96 in.3 96 in. cubed 16 in.3 16 in. cubed 144 in.3 144 in. cubed 24 in.3
The volume of a pyramid is given by the formula V = (1/3) * base area * height.
Since the prism and pyramid have congruent bases and height, the base area of the pyramid is the same as that of the prism.
Let the base area be A and the height be H. Since the volume of the pyramid is 48 in^3, we have:
48 = (1/3) * A * H
Multiplying both sides by 3 gives:
144 = A * H
The volume of the prism is given by the formula V = base area * height. Since the base area and height are the same as that of the pyramid, the volume of the prism is:
V = A * H = 144 in^3
Therefore, the volume of the prism is 144 in^3.
Therefore, the correct answer is:
144 in.3