A right pyramid has a volume of 156 m3. What is the volume of a right prism that has the same base and height as the pyramid?
To find the volume of the right prism with the same base and height as the pyramid, we need to find the volume of the prism.
The volume of a right pyramid is given by the formula V = (1/3) * base area * height.
Let's denote the base area as B and the height as h. Given that the volume of the pyramid is 156 m^3, we have:
V = (1/3) * B * h = 156.
Since the prism has the same base and height as the pyramid, the volume of the prism would be:
V_prism = B * h * h = B * h^2.
Given that the volume of the pyramid is 156 m^3, we can find the volume of the prism by rearranging the formula for the volume of the pyramid:
B * h^2 = 3 * V.
Substitute V = 156 into the equation:
B * h^2 = 3 * 156
B * h^2 = 468
Therefore, the volume of the prism is 468 m^3.