A rectangular pyramid has a volume of 420 inches cubed. If a rectangular prism has a base and height congruent to the pyramid, what is the volume of the prism?
Let the base of the rectangular pyramid be a rectangle with length x and width y, and let the height of the pyramid be h.
The volume of a pyramid is given by the formula V = (1/3) * base area * height. So, for the pyramid:
420 = (1/3) * xy * h
Now, since the base and height of the rectangular prism are congruent to the pyramid, the base area will also be xy and the height will be h.
Therefore, the volume of the rectangular prism will also be V = base area * height.
V = xy * h
From the equation for the pyramid, we know that xy * h = 420.
Therefore, the volume of the rectangular prism is also 420 inches cubed.