There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is 48in3, what is the volume of the prism?
The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height. Since the base of the pyramid and prism are congruent, the length and width of the prism are equal to the base dimensions of the pyramid.
The formula for the volume of a pyramid is V = (1/3)Bh, where B is the area of the base and h is the height. Since the volume of the pyramid is given as 48in3 and the height is equal to the height of the prism, we can write:
48 = (1/3)(B)(h)
48 = (1/3)(B)(h)
We can substitute B = lw from above and solve for B:
48 = (1/3)(lw)(h)
48 = (1/3)(lwh)
B = 3(48)/lwh
B = 144/in3
The volume of the rectangular prism is the base area times the height:
V = B(h)
V = 144h = 144h
Therefore, the volume of the rectangular prism is 144in3.