a rectangular prism has a volume of 27in. if a rectangular prism has a base and height congruent to the prism, what is the volume of the pyramid.
Since the rectangular prism has a volume of 27 in³, we know that the base area multiplied by the height of the prism equals 27.
Let's denote the base length and width of the prism as x, and the height of the prism as x as well. Therefore, the volume of the prism is:
x * x * x = x³ = 27
Solving for x:
x = ∛27
x = 3
Therefore, the base length and width of the prism are 3 in, and the height of the prism is 3 in as well.
To find the volume of the pyramid, we know that the volume of a pyramid is one-third of the volume of a rectangular prism with the same base and height.
V(pyramid) = 1/3 * V(prism)
V(pyramid) = 1/3 * 27 in³
V(pyramid) = 9 in³
Therefore, the volume of the pyramid is 9 in³.