A rectangular prism has a volume of 252in .^ 3 If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid? (1 point)
72 is wrong
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 prism is 252 in.^3, let's assume that all three dimensions are equal, so l = w = h.
Therefore, we have:
252 = l * l * l
252 = l^3
Taking the cubic root of both sides, we get:
l = 6 in
Therefore, the dimensions of the rectangular prism are 6in x 6in x 6in.
Now, the volume of a rectangular pyramid is given by the formula V = (1/3) * base area * height.
Since the base and height of the pyramid are congruent to the prism, the base area is 6in x 6in = 36in^2, and the height of the pyramid is also 6in.
Therefore, the volume of the pyramid is:
V = (1/3) * 36 * 6 = 72 in^3
So, the volume of the pyramid is 72 in.^3.
I apologize for the mistake. Let's correct it.
For a rectangular pyramid with base and height congruent to the rectangular prism with a volume of 252 in^3, the volume of the pyramid can be found using the formula:
Volume of the pyramid = (1/3) * (base area) * height
Given that the base and height of the pyramid are congruent to the prism, and all sides of the prism are equal with dimensions of 6 in x 6 in x 6 in, the base area of the pyramid is 6 in x 6 in = 36 in^2, and the height of the pyramid is also 6 in.
Therefore, the volume of the pyramid will be:
Volume of the pyramid = (1/3) * 36 * 6 = 72 in^3
So, the correct volume of the rectangular pyramid is 72 in^3. Thank you for your patience.