bot 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
154 cm3
154 cm cubed
952 cm3
952 cm cubed
448 cm3
The volume of the composite figure would be 616 cm3.
To calculate this, first find the volume of the rectangular prism:
Volume = length x width x height
Volume = 14 cm x 5 cm x 4 cm
Volume = 280 cm3
Then, find the volume of one triangular prism:
Volume = (1/2) x base x height x length
Volume = (1/2) x 5 cm x 6 cm x 4 cm
Volume = 60 cm3
Since there are two identical triangular prisms attached to the rectangular prism, multiply the volume of one by 2:
Total volume of triangular prisms = 2 x 60 cm3 = 120 cm3
Now, add the volume of the rectangular prism and the total volume of the triangular prisms together:
280 cm3 + 120 cm3 = 400 cm3
Therefore, the volume of the composite figure is 400 cm3.
okay but which one is equivalent to 400 cm3 because 400 cm3 isn't shown on the listed options
I apologize for the error. Let's correct the calculation.
The volume of the rectangular prism is:
Volume = length x width x height
Volume = 14 cm x 5 cm x 4 cm
Volume = 280 cm3
The volume of one triangular prism is:
Volume = (1/2) x base x height x length
Volume = (1/2) x 5 cm x 6 cm x 4 cm
Volume = 60 cm3
Since there are two identical triangular prisms attached to the rectangular prism, the total volume of the triangular prisms is:
Total volume of triangular prisms = 2 x 60 cm3 = 120 cm3
Now, add the volume of the rectangular prism and the total volume of the triangular prisms together:
280 cm3 + 120 cm3 = 400 cm3
Therefore, the volume of the composite figure is 400 cm3, which corresponds to the option that isn't listed. Apologies for the oversight.