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)
To find the volume of the composite figure, we first need to find the volume of each individual shape and then add them together.
The volume of a rectangular prism is calculated by multiplying the length, width, and height. So, for the rectangular prism:
Volume = length x width x height
Volume = 14 cm x 5 cm x 4 cm
Volume = 280 cm³
Next, we need to find the volume of one of the triangular prisms. The formula for the volume of a triangular prism is 1/2 x base x height x length. In this case, the base and height of the triangle are 5 cm and 6 cm respectively, and the length is 14 cm.
Volume = 1/2 x base x height x length
Volume = 1/2 x 5 cm x 6 cm x 14 cm
Volume = 210 cm³
Since there are two identical triangular prisms, the total volume of both is:
2 x 210 cm³ = 420 cm³
Finally, we add the volumes of the rectangular prism and the two triangular prisms to get the total volume of the composite figure:
Total Volume = 280 cm³ + 420 cm³
Total Volume = 700 cm³
Therefore, the volume of the composite figure is 700 cm³.
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
448 cm3
448 cm cubed
154 cm3
154 cm cubed
616 cm3
616 cm cubed
952 cm3
To find the volume of the composite figure, we first calculate the volume of the rectangular prism and then the volume of one triangular prism, and finally, we find the total volume.
1. Volume of the rectangular prism:
Volume = length x width x height
Volume = 14 cm x 5 cm x 4 cm
Volume = 280 cm³
2. Volume of one triangular prism:
The formula for the volume of a triangular prism is 1/2 x base x height x length. In this case, the base and height of the triangle are 5 cm and 6 cm respectively, and the length is 14 cm.
Volume = 1/2 x base x height x length
Volume = 1/2 x 5 cm x 6 cm x 14 cm
Volume = 210 cm³
Since there are two identical triangular prisms, the total volume of both is:
2 x 210 cm³ = 420 cm³
3. Total volume of the composite figure:
Total Volume = Volume of rectangular prism + Volume of two triangular prisms
Total Volume = 280 cm³ + 420 cm³
Total Volume = 700 cm³
Therefore, the correct answer is:
700 cm³
pick the answer i put and pick the right one
The correct answer based on the provided calculations and explanation is:
700 cm3
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
A 448 cm3
448 cm cubed
B 154 cm3
154 cm cubed
C 616 cm3
616 cm cubed
D 952 cm3
The correct answer is:
A. 448 cm3
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
370 cm3
370 cm cubed
170 cm3
170 cm cubed
850 cm3
850 cm cubed
725 cm3
725 cm cubed
To find the volume of the composite figure, we need to calculate the volume of each individual shape and then add them together.
1. Volume of the cuboid (rectangular prism):
Given the length is 10 cm, width (since it's the same as the side of a cube) is 5 cm, and height is 12 cm.
Volume = length x width x height
Volume of cuboid = 10 cm x 5 cm x 12 cm = 600 cm³
2. Volume of one cube (there are two identical cubes):
The formula for the volume of a cube is side x side x side. In this case, the side of the cube is 5 cm.
Volume of one cube = 5 cm x 5 cm x 5 cm = 125 cm³
Volume of both cubes = 2 x 125 cm³ = 250 cm³
Total Volume of the composite figure = Volume of cuboid + Volume of both cubes
Total Volume = 600 cm³ + 250 cm³
Total Volume = 850 cm³
Therefore, the volume of the composite figure is 850 cm³.
The correct response from the provided options is:
850 cm³