Volume of Composite 3D Figures Quick Check
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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
154 cm3
154 cm cubed
448 cm3
448 cm cubed
616 cm3
616 cm cubed
952 cm3
To solve for the volume of the composite figure, we first need to find the volume of the rectangular prism.
Volume of rectangular prism = 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 identical triangular prisms and then multiply by 2 since there are two of them.
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 4 cm
Volume of one triangular prism = 60 cm3
Volume of both triangular prisms = 2 x 60 cm3 = 120 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 + 120 cm3 = 400 cm3
Therefore, the correct response is missing from the options provided. The correct volume of the composite figure is 400 cm3.