Use the image to answer the question.

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

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

Answer 1

To calculate 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 of rectangular prism = 10 in x 10 in x 12 in
Volume of rectangular prism = 1,200 in^3

Volume of each triangular prism = (base x height)/2
Volume of each triangular prism = (8 in x 6 in)/2
Volume of each triangular prism = 24 in^3

Total volume of dollhouse = volume of rectangular prism + volume of two triangular prisms
Total volume of dollhouse = 1,200 in^3 + (2 x 24 in^3)
Total volume of dollhouse = 1,200 in^3 + 48 in^3
Total volume of dollhouse = 1,248 in^3

Therefore, the total volume of the dollhouse is 1,248 in^3.