Question
A rectangular prism has a volume of 27 in if the rectangular pyramid has a base and height congruent to the prism what is the volume of the pyramid
Answers
GPT 3.5
The volume of a rectangular prism is given by the formula: V = l × w × h, 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 have:
27 = l × w × h
Since the base and height of the rectangular pyramid are congruent to the prism, we can set l = w = h.
So, 27 = l × l × l
27 = l^3
l = 3 inches
Therefore, the dimensions of the rectangular prism are 3 inches × 3 inches × 3 inches.
Now, to calculate the volume of the rectangular pyramid, we use the formula: V = (1/3) × l × w × h
Substitute l = w = h = 3 inches into the formula:
V = (1/3) × 3 × 3 × 3
V = (1/3) × 27
V = 9 inches^3
Therefore, the volume of the rectangular pyramid is 9 cubic inches.
Given that the volume of the rectangular prism is 27 in^3, we have:
27 = l × w × h
Since the base and height of the rectangular pyramid are congruent to the prism, we can set l = w = h.
So, 27 = l × l × l
27 = l^3
l = 3 inches
Therefore, the dimensions of the rectangular prism are 3 inches × 3 inches × 3 inches.
Now, to calculate the volume of the rectangular pyramid, we use the formula: V = (1/3) × l × w × h
Substitute l = w = h = 3 inches into the formula:
V = (1/3) × 3 × 3 × 3
V = (1/3) × 27
V = 9 inches^3
Therefore, the volume of the rectangular pyramid is 9 cubic inches.