A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 24 cm, a width of 3 cm, and a height of 12 cm. The pyramid has a height of 21 cm. Find the volume of the composite space figure.
To find the volume of the composite space figure, we need to find the volume of the prism and the volume of the pyramid separately, and then add them together.
First, let's find the volume of the prism:
Volume of a rectangular prism = length x width x height
Volume = 24 cm x 3 cm x 12 cm = 864 cubic cm
Next, let's find the volume of the pyramid:
Volume of a rectangular pyramid = (1/3) x base area x height
The base of the pyramid is the same as the base of the prism, so the base area is 24 cm x 3 cm = 72 square cm
Volume = (1/3) x 72 cm x 21 cm = 504 cubic cm
Now, let's add the volumes of the prism and the pyramid to find the total volume of the composite space figure:
Total Volume = Prism Volume + Pyramid Volume
Total Volume = 864 cubic cm + 504 cubic cm = 1368 cubic cm
Therefore, the volume of the composite space figure is 1368 cubic cm.