Volume of Composite 3D Figures Quick Check
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Question
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An illustration shows a that is shaped like a rectangular prism with two triangular prisms placed on the top, one on each side. The width of the rectangular prism is 10 inches, and the height is 12 inches. The base length of the triangular prisms on the top of the house is 8 inches each. There is a 2-inch gap between the two triangular prisms. The perpendicular height of the triangular prisms is 6 inches. A window is drawn on the face of each triangular prism, and a door is drawn on the bottom center of the rectangular prism.
Write and solve an expression for the total volume of the dollhouse.(1 point)
Responses
264 in.3
264 in. cubed
2,400 in.3
2,400 in. cubed
2,640 in.3
2,640 in. cubed
3,120 in.3
3,120 in. cubed
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To find the total volume of the dollhouse, you need to calculate the volume of the rectangular prism and the volume of the two triangular prisms and then add them together.
Volume of rectangular prism = length x width x height
Volume of rectangular prism = 10 inches x 8 inches x 12 inches
Volume of rectangular prism = 960 cubic inches
Volume of one triangular prism = 1/2 x base length x base width x height
Volume of one triangular prism = 1/2 x 8 inches x 2 inches x 6 inches
Volume of one triangular prism = 48 cubic inches
Volume of two triangular prisms (since there are 2) = 48 cubic inches x 2 = 96 cubic inches
Total volume = Volume of rectangular prism + Volume of two triangular prisms
Total volume = 960 cubic inches + 96 cubic inches
Total volume = 1056 cubic inches
Therefore, the total volume of the dollhouse is 1056 cubic inches.
The closest response option provided is 1,200 in.3, so the correct answer is not listed.
pick an answers i gave u
I apologize for the confusion. Among the provided response options, the closest one to the calculated total volume of 1056 cubic inches is:
2,640 in.3
2,640 in. cubed
Therefore, the closest answer choice to the correct volume of the dollhouse is 2,640 in.3.