Volume of Composite 3D Figures Quick Check
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Question
Use the image to answer the question.
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
2,400 in.3
2,400 in. cubed
264 in.3
264 in. cubed
3,120 in.3
3,120 in. cubed
2,640 in.3
To find the total volume of the dollhouse, we need to find the volume of the rectangular prism and the volume of the two triangular prisms.
Volume of the rectangular prism = length x width x height
Volume of the rectangular prism = 10 in x 8 in x 12 in = 960 in^3
Volume of one triangular prism = (1/2) x base x height x length
Volume of one triangular prism = (1/2) x 8 in x 6 in x 8 in = 192 in^3
Volume of two triangular prisms = 192 in^3 + 192 in^3 = 384 in^3
Total volume of the dollhouse = volume of rectangular prism + volume of two triangular prisms
Total volume of the dollhouse = 960 in^3 + 384 in^3 = 1344 in^3
Therefore, the total volume of the dollhouse is 1344 in^3.