A rectangular prism has a volume of 27in^3 . If a rectangular pyramid has a base and height congruent to the prism , what is the volume of the pyramid?
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. Since the volume of the prism is 27in^3 and the base and height are congruent, we can set l = w = h.
Therefore, the volume of the prism is 27 = l*l*l = l^3. Solving for l gives us l = 3in.
Now, 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. Since the base of the pyramid is congruent to the prism, we have B = l*w = 3*3 = 9in^2.
Therefore, the volume of the pyramid is V = (1/3)*9*3 = 9in^3.
So, the volume of the pyramid is 9in^3.