Volume of Composite 3D Figures Quick Check
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Question
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
2,400 in.3
2,400 in. cubed
3,120 in.3
To find the total volume of the dollhouse, first calculate the volume of the rectangular prism:
Volume = length x width x height
Volume = 10in x 8in x 12in
Volume = 960in³
Next, calculate the volume of one of the triangular prisms:
Volume = (1/2) x base x height x length
Volume = (1/2) x 8in x 6in x 8in
Volume = 192in³
Since there are two triangular prisms, the total volume of the triangular prisms is 2 x 192in³ = 384in³
Finally, add the volumes of the rectangular prism and the two triangular prisms to find the total volume:
Total volume = 960in³ + 384in³
Total volume = 1344in³
Therefore, the total volume of the dollhouse is 1344 in.³.
wrong
I apologize for the error in my previous response. Let's recalculate the total volume of the dollhouse:
1. Calculate the volume of the rectangular prism:
Volume_rectangular_prism = length x width x height
Volume_rectangular_prism = 10in x 8in x 12in
Volume_rectangular_prism = 960in³
2. Calculate the volume of one of the triangular prisms:
Volume_triangular_prism = (1/2) x base x height x length
Volume_triangular_prism = (1/2) x 8in x 6in x 8in
Volume_triangular_prism = 192in³
3. Since there are two identical triangular prisms, the total volume of both triangular prisms is:
Total_volume_triangular_prisms = 2 x Volume_triangular_prism
Total_volume_triangular_prisms = 2 x 192in³
Total_volume_triangular_prisms = 384in³
4. Now, calculate the total volume of the dollhouse:
Total_volume_dollhouse = Volume_rectangular_prism + Total_volume_triangular_prisms
Total_volume_dollhouse = 960in³ + 384in³
Total_volume_dollhouse = 1344in³
Therefore, the correct total volume of the dollhouse is 1344 in.³. Thank you for your patience.