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.
Answer: ___in.^3
To find the total volume of the dollhouse, we need to find the volumes of the rectangular prism and the two triangular prisms separately and then add them together.
Volume of the rectangular prism:
Volume = length x width x height
Volume = 10 inches x 10 inches x 12 inches
Volume = 1200 cubic inches
Volume of one triangular prism:
Volume = 1/2 x base length x perpendicular height x width
Volume = 1/2 x 8 inches x 6 inches x 10 inches
Volume = 240 cubic inches
Total volume of the dollhouse:
Total volume = Volume of rectangular prism + 2 x Volume of one triangular prism
Total volume = 1200 cubic inches + 2 x 240 cubic inches
Total volume = 1200 cubic inches + 480 cubic inches
Total volume = 1680 cubic inches
Therefore, the total volume of the dollhouse is 1680 cubic inches.