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.
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 and the base and height are congruent, we can assume that the dimensions of the prism are all equal. Let's call the length, width, and height of the prism x.
Therefore, the volume of the prism can be expressed as x * x * x = x^3 = 27 in.^3.
Solving for x, we find that x = 3.
Since the base and height of the pyramid are congruent to the prism, the volume of the pyramid can be calculated using the formula V = (1/3)bh, where b is the area of the base and h is the height.
The base of the pyramid is a square with side length 3 inches. Therefore, the area of the base is 3 * 3 = 9 in.^2.
The height of the pyramid is also 3 inches.
Plugging in the values, we get V = (1/3) * 9 * 3 = 9 in.^3.
Therefore, the volume of the rectangular pyramid is 9 in.^3.
Given that the volume of the rectangular prism is 27 in.^3 and the base and height are congruent, we can assume that the dimensions of the prism are all equal. Let's call the length, width, and height of the prism x.
Therefore, the volume of the prism can be expressed as x * x * x = x^3 = 27 in.^3.
Solving for x, we find that x = 3.
Since the base and height of the pyramid are congruent to the prism, the volume of the pyramid can be calculated using the formula V = (1/3)bh, where b is the area of the base and h is the height.
The base of the pyramid is a square with side length 3 inches. Therefore, the area of the base is 3 * 3 = 9 in.^2.
The height of the pyramid is also 3 inches.
Plugging in the values, we get V = (1/3) * 9 * 3 = 9 in.^3.
Therefore, the volume of the rectangular pyramid is 9 in.^3.