A rectangular prism has a volume of 33 feet cubed. If a pyramid has a base and height congruent to the prism, what is the volume of the pyramid?

1 answer

To find the volume of the pyramid, we can use the formula for the volume of a pyramid:

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

Since the base and height of the pyramid are congruent to the prism, the base area of the pyramid will be the same as the base area of the prism.

Given that the volume of the prism is 33 feet cubed, we know that the volume of the pyramid is also equal to 33 feet cubed.

So, let's set up the equation:

33 = (1/3) * base area * height

33 = (1/3) * base area * base

33 = (1/3) * base^2 * base

33 = (1/3) * base^3

Multiplying both sides by 3 to isolate the base^3:

99 = base^3

Taking the cube root of both sides:

base = 4.62 feet

Therefore, the volume of the pyramid is 33 feet cubed.