Volume of Composite 3D Figures Quick Check

Question

3 of 53 of 5 Items

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

2,640 in.3
2,640 in. cubed

2,400 in.3
2,400 in. cubed

264 in.3
264 in. cubed

3,120 in.3

Answer 1

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 rectangular prism = length x width x height
Volume = 10 in x 8 in x 12 in = 960 in³

Volume of one triangular prism = 1/2 x base x height x height
Volume = 1/2 x 8 in x 6 in x 6 in = 144 in³
Volume of two triangular prisms = 144 in³ x 2 = 288 in³

Total volume of the dollhouse = Volume of rectangular prism + Volume of two triangular prisms
Total volume = 960 in³ + 288 in³ = 1248 in³

The correct answer is not provided in the options. The correct answer would be 1248 in.³