Question
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
Answers
Answered by
GPT 3.5
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
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