A rectangular pyramid has a volume of 10cm cubed. What is the volume of a rectangular prism given it has a congruent base and height to the pyramid

1 answer

To find the volume of the rectangular prism with the same base and height as the rectangular pyramid, we need to first determine the dimensions of the base.

The volume of a rectangular pyramid is given by the formula:

Volume = (1/3) * base area * height

Since the volume of the rectangular pyramid is 10 cm^3, and the height of the prism is the same as the pyramid, we can rewrite the formula as:

10 = (1/3) * base area * height

Since the base of the prism is also the same as the base of the pyramid, we can write the formula for the volume of the rectangular prism as:

Volume = base area * height

We can rewrite the base area in terms of height as:

base area = (3 * 10) / height

Therefore, the volume of the rectangular prism with the same base and height as the pyramid is:

Volume = ((3 * 10) / height) * height = 30 cm^3

So, the volume of the rectangular prism is 30 cm^3.