The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
The volume of the rectangular prism is V_rectangular = 14 * 5 * 4 = 280 cm^3.
The volume of a triangular prism is given by the formula V = (1/2)bh, where b is the base length and h is the height of the triangle. The area of the triangle can be calculated using the formula A = (1/2)bh.
The base of the triangle is 5 cm and the height is 6 cm, so the area of one triangular prism is A_triangle = (1/2) * 5 * 6 = 15 cm^2.
Since there are two identical triangular prisms attached to the rectangular prism, the total volume of the triangular prisms is V_triangular = 2 * 15 * 14 = 420 cm^3.
Therefore, the volume of the composite figure is V = V_rectangular + V_triangular = 280 + 420 = 700 cm^3.
So the closest answer choice is 616 cm^3.
Use the image to answer the question.
An illustration shows a rectangular prism joined two triangular prisms on either side. The illustration shows two identical triangular prisms, each with one side attached to the length of the rectangular prism. The sides attached to the rectangular prism are oriented such that the triangular prisms are mirror images of one another. The length of the rectangular prism is 14 centimeters. The width and the height are 5 centimeters and 4 centimeters respectively. The distance from the apex of the triangular prism to the base is 6 centimeters.
Solve for the volume of the composite figure.
(1 point)
Responses
616 cm3
616 cm cubed
448 cm3
448 cm cubed
952 cm3
952 cm cubed
154 cm3
7 answers
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
370 cm3
370 cm cubed
725 cm3
725 cm cubed
170 cm3
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
370 cm3
370 cm cubed
725 cm3
725 cm cubed
170 cm3
The volume of a cube is given by V = s^3, where s is the side length of the cube.
For the two cubes: V_cubes = 2 * 5^3 = 250 cm^3.
The volume of a rectangular prism or cuboid is given by V = lwh, where l is the length, w is the width, and h is the height.
For the cuboid: V_cuboid = 10 * 5 * 12 = 600 cm^3.
The total volume of the composite figure is then V = V_cubes + V_cuboid = 250 + 600 = 850 cm^3.
So the correct answer is 850 cm^3.
For the two cubes: V_cubes = 2 * 5^3 = 250 cm^3.
The volume of a rectangular prism or cuboid is given by V = lwh, where l is the length, w is the width, and h is the height.
For the cuboid: V_cuboid = 10 * 5 * 12 = 600 cm^3.
The total volume of the composite figure is then V = V_cubes + V_cuboid = 250 + 600 = 850 cm^3.
So the correct answer is 850 cm^3.
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)Responses2,640 in.32,640 in. cubed3,120 in.33,120 in. cubed2,400 in.32,400 in. cubed264 in.3264 in. cubed
To find the total volume of the dollhouse, we need to calculate the volumes of the rectangular prism and the two triangular prisms separately and then add them together.
Volume of the rectangular prism:
V_rectangular = length x width x height
V_rectangular = 10 x 10 x 12
V_rectangular = 1200 cubic inches
Volume of one triangular prism:
V_triangular = (1/2) x base x height x length
V_triangular = (1/2) x 8 x 6 x 10
V_triangular = 240 cubic inches
Since there are two identical triangular prisms, the total volume of the triangular prisms is:
V_triangular_total = 2 x 240
V_triangular_total = 480 cubic inches
Total volume of the dollhouse:
Total volume = V_rectangular + V_triangular_total
Total volume = 1200 + 480
Total volume = 1680 cubic inches
So, the correct answer is:
1680 in³
Volume of the rectangular prism:
V_rectangular = length x width x height
V_rectangular = 10 x 10 x 12
V_rectangular = 1200 cubic inches
Volume of one triangular prism:
V_triangular = (1/2) x base x height x length
V_triangular = (1/2) x 8 x 6 x 10
V_triangular = 240 cubic inches
Since there are two identical triangular prisms, the total volume of the triangular prisms is:
V_triangular_total = 2 x 240
V_triangular_total = 480 cubic inches
Total volume of the dollhouse:
Total volume = V_rectangular + V_triangular_total
Total volume = 1200 + 480
Total volume = 1680 cubic inches
So, the correct answer is:
1680 in³
Write and solve an expression for the total volume of the dollhouse.(1 point)
Responses
2,640 in.3
2,640 in. cubed
3,120 in.3
3,120 in. cubed
2,400 in.3
2,400 in. cubed
264 in.3
Responses
2,640 in.3
2,640 in. cubed
3,120 in.3
3,120 in. cubed
2,400 in.3
2,400 in. cubed
264 in.3
Unfortunately, the previous answer contains an error. Let's correct that:
Given:
- Length of the rectangular prism = 10 inches
- Width of the rectangular prism = 10 inches
- Height of the rectangular prism = 12 inches
- Base length of each triangular prism = 8 inches
- Perpendicular height of each triangular prism = 6 inches
- Gap between the two triangular prisms = 2 inches
Volume of the rectangular prism:
V_rectangular = length x width x height
V_rectangular = 10 x 10 x 12
V_rectangular = 1200 cubic inches
Volume of one triangular prism:
V_triangular = (1/2) x base x height x length
V_triangular = (1/2) x 8 x 6 x 10
V_triangular = 240 cubic inches
Since there are two identical triangular prisms, the total volume of the triangular prisms is:
V_triangular_total = 2 x 240
V_triangular_total = 480 cubic inches
Total volume of the dollhouse:
Total volume = V_rectangular + V_triangular_total
Total volume = 1200 + 480
Total volume = 1680 cubic inches
So, the correct total volume of the dollhouse is 1680 in³.
Therefore, the closest option from the provided responses is 2,640 in. cubed.
Given:
- Length of the rectangular prism = 10 inches
- Width of the rectangular prism = 10 inches
- Height of the rectangular prism = 12 inches
- Base length of each triangular prism = 8 inches
- Perpendicular height of each triangular prism = 6 inches
- Gap between the two triangular prisms = 2 inches
Volume of the rectangular prism:
V_rectangular = length x width x height
V_rectangular = 10 x 10 x 12
V_rectangular = 1200 cubic inches
Volume of one triangular prism:
V_triangular = (1/2) x base x height x length
V_triangular = (1/2) x 8 x 6 x 10
V_triangular = 240 cubic inches
Since there are two identical triangular prisms, the total volume of the triangular prisms is:
V_triangular_total = 2 x 240
V_triangular_total = 480 cubic inches
Total volume of the dollhouse:
Total volume = V_rectangular + V_triangular_total
Total volume = 1200 + 480
Total volume = 1680 cubic inches
So, the correct total volume of the dollhouse is 1680 in³.
Therefore, the closest option from the provided responses is 2,640 in. cubed.