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
264 in.3
264 in. cubed
3,120 in.3
3,120 in. cubed
2,400 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 = 10 in x 8 in x 12 in = 960 in³
Volume of one triangular prism:
1/2 x Base x Height x Width = 1/2 x 8 in x 6 in x 12 in = 288 in³
Volume of both triangular prisms:
288 in³ + 288 in³ = 576 in³
Total volume of the dollhouse:
960 in³ (rectangular prism) + 576 in³ (both triangular prisms) = 1,536 in³
Therefore, the total volume of the dollhouse is 1,536 in³.