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A solid rectangular right prism is 10 inches long, 9 inches high, and 9 inches deep. At one square base of the prism, a 2 inch high square pyramid is cut from the prism. At the opposite square base of the prism, a square pyramid measuring 3 inches high is added. The bases of the pyramids are the same size as the square bases of the rectangular prism.

What is the volume of the composite figure?

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in³

2 Answers

4 votes

Answer:

837

Explanation:

User Giorgos Manoltzas
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The rectangular prism has a volume of length x width x height = 10 in x 9 in x 9 in = 810 cubic inches.

The pyramid that is cut from the prism has a volume of (1/3) x base area x height = (1/3) x 9 in² x 2 in = 6 in³.

The pyramid that is added to the opposite base has a volume of (1/3) x base area x height = (1/3) x 9 in² x 3 in = 9 in³.

The composite figure is formed by removing a pyramid with volume 6 in³ from the rectangular prism and adding a pyramid with volume 9 in³ to the opposite base. The resulting figure is still a rectangular prism, with the same length and width, but a slightly different height.

The height of the rectangular prism is reduced by 2 inches (the height of the pyramid that was cut), and then increased by 3 inches (the height of the pyramid that was added). So, the new height of the rectangular prism is:

9 in - 2 in + 3 in = 10 in

The volume of the composite figure is then:

Volume = length x width x height = 10 in x 9 in x 10 in = 900 cubic inches.

Therefore, the volume of the composite figure is 900 cubic inches.
User Irfan Ashraf
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