A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 12 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.

Question

(1 point)
Responses

480 in.3
480 in. 3

300 in.3
300 in. 3

2400 in.3
2400 in. 3

400 in.3

Answer 1

First, find the volume of the prism:
Volume of prism = length x width x height
Volume = 12 in. x 4 in. x 5 in.
Volume = 240 in.3

Next, find the volume of the pyramid:
Volume of pyramid = 1/3 x base area x height
Base area = length x width = 12 in. x 4 in. = 48 in.2
Volume = 1/3 x 48 in.2 x 10 in.
Volume = 160 in.3

Add the volumes of the prism and pyramid to find the total volume of the composite space figure:
Total volume = Volume of prism + Volume of pyramid
Total volume = 240 in.3 + 160 in.3
Total volume = 400 in.3

Therefore, the total volume of the composite space figure is 400 in.3.