A rectangular prism has a volume of 27 in.3 . If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?(1 point) in.3
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Given that the volume of the prism is 27 in^3, we can write the equation as 27 = lwh. Since the base and height of the pyramid are congruent to the prism, the base of the pyramid will have the same dimensions as the base of the prism.
The volume of a rectangular pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. Since the base of the pyramid is congruent to the prism, the base area B will be the same as that of the prism, which is lw.
Therefore, the volume of the pyramid is V = (1/3)(lw)h. Since h is congruent to the height of the prism, we can substitute h = l in the formula.
V = (1/3)(lw)l
V = (1/3)l^2w
Since we are given that the volume of the prism is 27 in^3, we know that lw = 27. Substituting this into the formula for the volume of the pyramid:
V = (1/3)(27) = 9 in^3
Therefore, the volume of the pyramid is 9 in^3.