Question

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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)

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, we calculate the volume of the rectangular prism:

Volume of rectangular prism = width x height x base length
Volume of rectangular prism = 10 inches x 12 inches x 8 inches
Volume of rectangular prism = 960 cubic inches

Next, we calculate the volume of one of the triangular prisms:
Volume of one triangular prism = (1/2) x base length x perpendicular height x base length
Volume of one triangular prism = (1/2) x 8 inches x 6 inches x 8 inches
Volume of one triangular prism = 192 cubic inches

Since there are two triangular prisms on the top of the dollhouse, we need to calculate the total volume of both:
Total volume of the two triangular prisms = 192 cubic inches + 192 cubic inches
Total volume of the two triangular prisms = 384 cubic inches

Finally, we find the total volume of the dollhouse by adding the volume of the rectangular prism and the total volume of the two triangular prisms:
Total volume of the dollhouse = 960 cubic inches + 384 cubic inches
Total volume of the dollhouse = 1344 cubic inches

So, the expression for the total volume of the dollhouse is 1344 cubic inches.