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
792 cm 3
To find the volume of the composite space figure, we need to add the volumes of the rectangular prism and the rectangular pyramid.
The volume of the rectangular prism is given by length x width x height:
Volume of rectangular prism = 24 cm x 3 cm x 12 cm = 864 cm³
The volume of the rectangular pyramid is given by 1/3 x base area x height:
The base area of the pyramid is equal to the length x width of the rectangular prism:
Base area of rectangular pyramid = 24 cm x 3 cm = 72 cm²
Volume of rectangular pyramid = 1/3 x 72 cm² x 21 cm = 504 cm³
The total volume of the composite space figure is the sum of the volumes of the rectangular prism and the rectangular pyramid:
Total volume = 864 cm³ + 504 cm³ = 1368 cm³
So, the correct answer is 1,368 cm³.