To find the total volume of the dollhouse, we need to calculate the volume of the rectangular prism and the two triangular prisms separately, and then add them together.
Volume of rectangular prism: 10 in (width) x 12 in (height) x 8 in (base length of triangles on top) = 960 in^3
Volume of one triangular prism: 1/2 x 8 in (base length) x 6 in (perpendicular height) x 8 in (base length) = 192 in^3
Volume of two triangular prisms: 2 x 192 in^3 = 384 in^3
Total volume of the dollhouse: 960 in^3 (rectangular prism) + 384 in^3 (two triangular prisms) = 1,344 in^3
The correct answer is not provided in the options. The correct answer is 1,344 in^3.
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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)
Responses
2,640 in.3
2,640 in. cubed
2,400 in.3
2,400 in. cubed
264 in.3
264 in. cubed
3,120 in.3
5 answers
Write and solve an expression for the total volume of the dollhouse.(1 point)
Responses
2,640 in.^3
2,400 in.^3
264 in.^3
3,120 in.^3
Responses
2,640 in.^3
2,400 in.^3
264 in.^3
3,120 in.^3
To find the total volume of the dollhouse, we need to calculate the volume of the rectangular prism and the two triangular prisms separately, and then add them together.
Volume of rectangular prism: 10 in (width) x 12 in (height) x 8 in (base length of triangles on top) = 960 in^3
Volume of one triangular prism: 1/2 x 8 in (base length) x 6 in (perpendicular height) x 8 in (base length) = 192 in^3
Volume of two triangular prisms: 2 x 192 in^3 = 384 in^3
Total volume of the dollhouse: 960 in^3 (rectangular prism) + 384 in^3 (two triangular prisms) = 1,344 in^3
Therefore, the correct answer is not provided in the options. The correct total volume of the dollhouse is 1,344 in^3.
Volume of rectangular prism: 10 in (width) x 12 in (height) x 8 in (base length of triangles on top) = 960 in^3
Volume of one triangular prism: 1/2 x 8 in (base length) x 6 in (perpendicular height) x 8 in (base length) = 192 in^3
Volume of two triangular prisms: 2 x 192 in^3 = 384 in^3
Total volume of the dollhouse: 960 in^3 (rectangular prism) + 384 in^3 (two triangular prisms) = 1,344 in^3
Therefore, the correct answer is not provided in the options. The correct total volume of the dollhouse is 1,344 in^3.
not the answer choice
Apologies for the confusion. Let's calculate the total volume of the dollhouse using the information provided.
Volume of the rectangular prism: 10 in (width) x 12 in (height) x 8 in (base length of triangles on top) = 960 in^3
Volume of each triangular prism: 1/2 x 8 in (base length) x 6 in (perpendicular height) x 8 in (base length) = 192 in^3
Volume of both triangular prisms: 2 x 192 in^3 = 384 in^3
Total volume of the dollhouse: 960 in^3 (rectangular prism) + 384 in^3 (two triangular prisms) = 1,344 in^3
Therefore, the total volume of the dollhouse is 1,344 in^3. The correct answer is not provided in the options given.
Volume of the rectangular prism: 10 in (width) x 12 in (height) x 8 in (base length of triangles on top) = 960 in^3
Volume of each triangular prism: 1/2 x 8 in (base length) x 6 in (perpendicular height) x 8 in (base length) = 192 in^3
Volume of both triangular prisms: 2 x 192 in^3 = 384 in^3
Total volume of the dollhouse: 960 in^3 (rectangular prism) + 384 in^3 (two triangular prisms) = 1,344 in^3
Therefore, the total volume of the dollhouse is 1,344 in^3. The correct answer is not provided in the options given.
3 answers