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
To find the volume of the composite space figure, we first calculate the volume of the prism:
Volume of prism = length x width x height
Volume of prism = 24 cm x 3 cm x 12 cm
Volume of prism = 864 cm³
Next, we calculate the volume of the pyramid:
Volume of 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 cm²
Volume of pyramid = 1/3 x 72 cm² x 21 cm
Volume of pyramid = 504 cm³
Add the volumes of the prism and pyramid to get the total volume of the composite space figure:
Total volume = volume of prism + volume of pyramid
Total volume = 864 cm³ + 504 cm³
Total volume = 1368 cm³
The volume of the composite space figure is 1368 cm³.