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
952 cm3
952 cm cubed
616 cm3
616 cm cubed
154 cm3
154 cm cubed
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The volume of the rectangular prism can be calculated by V = lwh, where l is the length, w is the width, and h is the height. Plugging in the values given, we get:
V_rectangular prism = 14 cm * 5 cm * 4 cm
V_rectangular prism = 280 cm^3
The volume of a triangular prism can be calculated by V = (1/2) * b * h * l, where b is the base, h is the height, and l is the length from the apex to the base. Since the two triangular prisms are identical, we can calculate the volume of one triangular prism and then multiply by 2.
V_triangular prism = (1/2) * 5 cm * 6 cm * 4 cm
V_triangular prism = 60 cm^3
Now, to find the volume of the composite figure, we add the volume of the rectangular prism and the volume of two triangular prisms:
V_composite figure = V_rectangular prism + 2 * V_triangular prism
V_composite figure = 280 cm^3 + 2 * 60 cm^3
V_composite figure = 280 cm^3 + 120 cm^3
V_composite figure = 400 cm^3
Therefore, the volume of the composite figure is 400 cm^3.
None of the provided responses are correct.
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616 cm3
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Sure!
The volume of the rectangular prism can be calculated by V = lwh, where l is the length, w is the width, and h is the height. Plugging in the values given, we get:
V_rectangular prism = 14 cm * 5 cm * 4 cm
V_rectangular prism = 280 cm^3
The volume of a triangular prism can be calculated by V = (1/2) * b * h * l, where b is the base, h is the height, and l is the length from the apex to the base. Since the two triangular prisms are identical, we can calculate the volume of one triangular prism and then multiply by 2.
V_triangular prism = (1/2) * 5 cm * 6 cm * 4 cm
V_triangular prism = 60 cm^3
Now, to find the volume of the composite figure, we add the volume of the rectangular prism and the volume of two triangular prisms:
V_composite figure = V_rectangular prism + 2 * V_triangular prism
V_composite figure = 280 cm^3 + 2 * 60 cm^3
V_composite figure = 280 cm^3 + 120 cm^3
V_composite figure = 400 cm^3
Therefore, the correct volume of the composite figure is 400 cm^3, not 616 cm^3. Thank you for bringing that to my attention.