Use the image to answer the question.
An illustration showing two cubes joined on both sides of a cuboid. The sides of the cube are 5 centimeters. The length of the cuboid is 10 centimeters and height is 12 centimeters.
What is the volume of the composite figure?
(1 point)
Responses
850 cm3
850 cm cubed
725 cm3
725 cm cubed
170 cm3
170 cm cubed
370 cm3
5 answers
725 cm3
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
264 in.3
264 in. cubed
2,640 in.3
2,640 in. cubed
2,400 in.3
2,400 in. cubed
3,120 in.3
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
264 in.3
264 in. cubed
2,640 in.3
2,640 in. cubed
2,400 in.3
2,400 in. cubed
3,120 in.3
To calculate the total volume of the dollhouse, we need to find the volume of each component and then add them together.
Volume of rectangular prism:
Volume = length x width x height
Volume = 10 in x 10 in x 12 in
Volume = 1200 in^3
Volume of one triangular prism:
Volume = 1/2 x base x height x length
Volume = 1/2 x 8 in x 6 in x 10 in
Volume = 240 in^3
Total volume:
Total volume = 2 x (Volume of one triangular prism) + Volume of rectangular prism
Total volume = 2 x 240 in^3 + 1200 in^3
Total volume = 480 in^3 + 1200 in^3
Total volume = 1680 in^3
Therefore, the total volume of the dollhouse is 1680 in^3.
Volume of rectangular prism:
Volume = length x width x height
Volume = 10 in x 10 in x 12 in
Volume = 1200 in^3
Volume of one triangular prism:
Volume = 1/2 x base x height x length
Volume = 1/2 x 8 in x 6 in x 10 in
Volume = 240 in^3
Total volume:
Total volume = 2 x (Volume of one triangular prism) + Volume of rectangular prism
Total volume = 2 x 240 in^3 + 1200 in^3
Total volume = 480 in^3 + 1200 in^3
Total volume = 1680 in^3
Therefore, the total volume of the dollhouse is 1680 in^3.
WRONG
I apologize for the error in my previous response. Let's calculate the total volume of the dollhouse again.
Volume of rectangular prism:
Volume = length x width x height
Volume = 10 in x 10 in x 12 in
Volume = 1200 in^3
Volume of one triangular prism:
Volume = 1/2 x base x height x length
Volume = 1/2 x 8 in x 6 in x 10 in
Volume = 240 in^3
Total volume of both triangular prisms:
Total volume of the two triangular prisms = 2 x Volume of one triangular prism
Total volume of the two triangular prisms = 2 x 240 in^3
Total volume of the two triangular prisms = 480 in^3
Total volume of the dollhouse:
Total volume = Volume of rectangular prism + Total volume of the two triangular prisms
Total volume = 1200 in^3 + 480 in^3
Total volume = 1680 in^3
Therefore, the total volume of the dollhouse is 1680 in^3.
Volume of rectangular prism:
Volume = length x width x height
Volume = 10 in x 10 in x 12 in
Volume = 1200 in^3
Volume of one triangular prism:
Volume = 1/2 x base x height x length
Volume = 1/2 x 8 in x 6 in x 10 in
Volume = 240 in^3
Total volume of both triangular prisms:
Total volume of the two triangular prisms = 2 x Volume of one triangular prism
Total volume of the two triangular prisms = 2 x 240 in^3
Total volume of the two triangular prisms = 480 in^3
Total volume of the dollhouse:
Total volume = Volume of rectangular prism + Total volume of the two triangular prisms
Total volume = 1200 in^3 + 480 in^3
Total volume = 1680 in^3
Therefore, the total volume of the dollhouse is 1680 in^3.