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.
(1 point)
Responses
4,032 cm3
4,032 cm 3
2,376 cm3
2,376 cm 3
1,368 cm3
1,368 cm 3
792 cm3
It has to be one of the following answer choices.
To find the volume of the composite space figure, we need to find the volume of both the rectangular prism and the rectangular pyramid separately, and then add them together.
The volume of the rectangular prism is found by multiplying its length, width, and height:
Volume of prism = 24 cm * 3 cm * 12 cm = 864 cm^3
The volume of the rectangular pyramid is found by multiplying its base area (length * width) by its height, and then dividing by 3:
Volume of pyramid = (24 cm * 3 cm * 21 cm) / 3 = 1,008 cm^3
The total volume of the composite space figure is then:
Total volume = Volume of prism + Volume of pyramid
Total volume = 864 cm^3 + 1,008 cm^3 = 1,872 cm^3
Therefore, the correct answer is 1,872 cm^3.