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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

264 in.3
264 in. cubed

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

3,120 in.3
3,120 in. cubed
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Answer 1

To calculate the total volume of the dollhouse, we first calculate the volume of the rectangular prism:
Volume = length x width x height
Volume = 10 x 10 x 12
Volume = 1200 in. cubed

Next, we calculate the volume of one of the triangular prisms:
Volume = 1/2 x base length x perpendicular height x width
Volume = 1/2 x 8 x 6 x 10
Volume = 240 in. cubed

Since there are two triangular prisms, we calculate the total volume for both:
Total volume for triangular prisms = 2 x 240
Total volume for triangular prisms = 480 in. cubed

Finally, we add the volume of the rectangular prism and the volume of the two triangular prisms to get the total volume of the dollhouse:
Total volume = 1200 + 480
Total volume = 1680 in. cubed

Therefore, the correct answer is not listed, the total volume of the dollhouse is 1680 in. cubed.