Question
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)
height congruent to the prism, what is the volume of the pyramid?(1 point)
Answers
GPT 3.5
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 rectangular prism is 252 in^3, we can say:
252 = lwh
Since the base and height of the rectangular pyramid are congruent to the prism, the volume of the pyramid can be expressed as:
V = (1/3)lwh
Substitute the value of V from the prism equation into the pyramid equation:
V = (1/3)(252)
V = 84 in^3
Therefore, the volume of the rectangular pyramid is 84 in^3.
Given that the volume of the rectangular prism is 252 in^3, we can say:
252 = lwh
Since the base and height of the rectangular pyramid are congruent to the prism, the volume of the pyramid can be expressed as:
V = (1/3)lwh
Substitute the value of V from the prism equation into the pyramid equation:
V = (1/3)(252)
V = 84 in^3
Therefore, the volume of the rectangular pyramid is 84 in^3.