Question
A rectangular prism has a volume of 27 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
 in.3
Answers
GPT 3.5
The volume of a rectangular prism is calculated using the formula V = lwh, where l is the length, w is the width, and h is the height.
Given that the volume of the rectangular prism is 27 in^3, we can set up the equation as follows:
V(prism) = l * w * h
27 = l * w * h
Since the base and height of the rectangular pyramid are congruent to the prism, the volume of the pyramid will be one-third of the volume of the prism. Therefore, the volume of the pyramid is:
V(pyramid) = (1/3) * V(prism)
V(pyramid) = (1/3) * 27
V(pyramid) = 9 in^3
Therefore, the volume of the pyramid is 9 in^3.
Given that the volume of the rectangular prism is 27 in^3, we can set up the equation as follows:
V(prism) = l * w * h
27 = l * w * h
Since the base and height of the rectangular pyramid are congruent to the prism, the volume of the pyramid will be one-third of the volume of the prism. Therefore, the volume of the pyramid is:
V(pyramid) = (1/3) * V(prism)
V(pyramid) = (1/3) * 27
V(pyramid) = 9 in^3
Therefore, the volume of the pyramid is 9 in^3.