The volume of a rectangular prism is equal to the base area multiplied by the height. Since the volume of the rectangular prism is 252 in^3 and the base and height are congruent, we can represent the volume of the rectangular prism as:
Volume of rectangular prism = base area * height
252 in^3 = base area * height
Since the base and height of the rectangular prism are congruent, we can represent the base area as the square of the length of the base:
base area = base * base = base^2
Therefore, we can rewrite the volume of the rectangular prism equation as:
252 in^3 = base^2 * height
Since we are looking for the volume of a rectangular pyramid with the same base and height as the rectangular prism, we can use the formula for the volume of a pyramid:
Volume of rectangular pyramid = (1/3) * base area * height
Now, substituting the expression for base area (base^2) from the equation for the volume of the rectangular prism into the formula for the volume of the pyramid, we have:
Volume of rectangular pyramid = (1/3) * base^2 * height
Since we know that the volume of the rectangular prism is 252 in^3, we can substitute that value in for the base^2 * height:
Volume of rectangular pyramid = (1/3) * 252 in^3
Volume of rectangular pyramid = 84 in^3
Therefore, the volume of the rectangular pyramid with the base and height congruent to the rectangular prism is 84 in^3.
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)
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1 answer