A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 15 cm, a width of 5 cm, and a height of 7 cm. The pyramid has a height of 13 cm. Find the volume of the composite space figure.
A. 1,500 cm^3
B. 500 cm^3
C. 975 cm^3
D. 850 cm^3
The base of the pyramid must be the same as the base of the prism, which is 15 x 5 = 75 cm^2. The volume of the pyramid is (1/3)bh, where b is the area of the base and h is the height. So, the volume of the pyramid is (1/3)(75)(13) = 325 cm^3.
The total volume of the composite figure is the sum of the volume of the prism and the volume of the pyramid:
V = (15)(5)(7) + 325
V = 525 + 325
V = 850 cm^3
Therefore, the answer is D. 850 cm^3.