Use the image to answer the question.
An illustration shows a composite figure of a tall vertical rectangular prism attached at the bottom right side to the base of a small triangular prism. The length and width of the rectangular prism are 75 feet each, and the height is 360 feet. The length of the triangular prism base is same as the length of the rectangular prism, as they are aligned. The perpendicular length from the apex to the base of the triangular prism is 80 feet. The height of the triangular prism is 25 feet.
Solve for the total volume of this hotel with an enclosed front lobby.
(1 point)
Responses
2,250,000 ft.3
2,250,000 ft. cubed
2,025,000 ft.3
2,025,000 ft. cubed
2,062,000 ft.3
2,062,000 ft. cubed
2,100,000 ft.3
To find the total volume of the hotel with an enclosed front lobby, we need to find the volume of both the rectangular prism and the triangular prism, then add them together.
Volume of rectangular prism = length x width x height
Volume of rectangular prism = 75 ft x 75 ft x 360 ft
Volume of rectangular prism = 2,025,000 cubic feet
Volume of triangular prism = (1/2) x base x height x length
Volume of triangular prism = (1/2) x 75 ft x 80ft x 25ft
Volume of triangular prism = 75,000 cubic feet
Total volume = volume of rectangular prism + volume of triangular prism
Total volume = 2,025,000 cubic feet + 75,000 cubic feet
Total volume = 2,100,000 cubic feet
Therefore, the total volume of the hotel with an enclosed front lobby is 2,100,000 ft.3.