A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 14 in, a width of 4 in and a height of 5 in. The pyramid has a height of 10 in. Find the volume of the composite space figure. Round your answer to the nearest hundredth.
To find the volume of the composite figure, we first need to find the volume of the prism and the volume of the pyramid separately.
Volume of the prism:
Volume = length × width × height
Volume = 14 in × 4 in × 5 in
Volume = 280 in³
Volume of the pyramid:
Volume = 1/3 × base area × height
First, we need to find the base area of the pyramid, which is the same as the base area of the prism since they are the same shape and size.
Base area = length × width
Base area = 14 in × 4 in
Base area = 56 in²
Now we can find the volume of the pyramid:
Volume = 1/3 × 56 in² × 10 in
Volume = 186.67 in³
Now, we can find the total volume of the composite space figure by adding the volume of the prism and the volume of the pyramid:
Total Volume = Volume of prism + Volume of pyramid
Total Volume = 280 in³ + 186.67 in³
Total Volume = 466.67 in³
Therefore, the volume of the composite space figure is approximately 466.67 cubic inches.