Question
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
952 cm3
952 cm cubed
448 cm3
448 cm cubed
154 cm3
To solve for the volume of the composite figure, we first need to calculate the volume of each individual shape and then add them together.
Volume of rectangular prism = length x width x height
Volume of rectangular prism = 14 cm x 5 cm x 4 cm
Volume of rectangular prism = 280 cm3
Volume of triangular prism = (1/2) x base x height x length
Volume of one triangular prism = (1/2) x 5 cm x 6 cm x 14 cm
Volume of one triangular prism = 210 cm3
Since there are two identical triangular prisms, the total volume of both triangular prisms = 2 x 210 cm3 = 420 cm3
Therefore, the total volume of the composite figure = volume of rectangular prism + volume of both triangular prisms
Total volume = 280 cm3 + 420 cm3
Total volume = 700 cm3
Thus, the correct answer is not provided in the options.
incorect
I apologize for the mistake in my previous response. Let's recalculate the volume of the composite figure using the correct formula for the volume of a triangular prism.
The volume of the composite figure consists of the rectangular prism and two triangular prisms.
1. Volume of Rectangular Prism:
Volume of rectangular prism = length x width x height
Volume of rectangular prism = 14 cm x 5 cm x 4 cm
Volume of rectangular prism = 280 cm³
2. Volume of Triangular Prism:
Volume of one triangular prism = (1/2) x base x height x length
Volume of one triangular prism = (1/2) x 5 cm x 6 cm x 14 cm
Volume of one triangular prism = 210 cm³
Since there are two identical triangular prisms, the total volume of both triangular prisms = 2 x 210 cm3 = 420 cm³
Total Volume of the composite figure = Volume of rectangular prism + Volume of both triangular prisms
Total Volume = 280 cm³ + 420 cm³
Total Volume = 700 cm³
Therefore, the correct volume of the composite figure is 700 cm³. Thank you for your patience.
use one of the anwers
Apologies for my previous responses. Let's use one of the provided answers to check if it is correct.
Let's use the answer: 616 cm^3
Volume of rectangular prism = length x width x height
Volume of rectangular prism = 14 cm x 5 cm x 4 cm
Volume of rectangular prism = 280 cm^3
Volume of one triangular prism = (1/2) x base x height x length
Volume of one triangular prism = (1/2) x 5 cm x 6 cm x 14 cm
Volume of one triangular prism = 210 cm^3
Total volume of both triangular prisms = 2 x 210 cm^3 = 420 cm^3
Total volume = Volume of rectangular prism + Volume of both triangular prisms
Total volume = 280 cm^3 + 420 cm^3
Total volume = 700 cm^3
As the answer 616 cm^3 is not equal to the correct volume of the composite figure calculated (700 cm^3), it seems that the other provided answer options are incorrect in this case.