Calculate the volume of the figure.
A three-dimensional figure is composed of a rectangular prism with a length of 3 cm, a width of 3 cm, and a height of 3 cm. One of the sides of the prism is also the base of a pyramid. This pyramid has a height of 2 cm.
(1 point)
Responses
15 cm³
15 cm³
33 cm³
33 cm³
45 cm³
45 cm³
54 cm³
54 cm³
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To calculate the volume of the figure, we need to find the volume of the rectangular prism and the volume of the pyramid separately, and then add them together.
The volume of the rectangular prism can be calculated using the formula:
Volume = length x width x height
Volume of rectangular prism = 3 cm x 3 cm x 3 cm = 27 cm³.
The volume of the pyramid can be calculated using the formula:
Volume = (1/3) x base area x height
Since one of the sides of the prism is the base of the pyramid, the base area is equal to 3 cm x 3 cm = 9 cm².
Volume of pyramid = (1/3) x 9 cm² x 2 cm = 6 cm³.
Therefore, the volume of the figure is 27 cm³ + 6 cm³ = 33 cm³.
The correct answer is 33 cm³.