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 find the volume of the rectangular prism. The formula for the volume of a rectangular prism is length x width x height.
Volume of rectangular prism = 14 cm x 5 cm x 4 cm
Volume of rectangular prism = 280 cm^3
Next, we find the volume of one triangular prism. The formula for the volume of a triangular prism is 1/2 x base x height x length.
Volume of one triangular prism = 1/2 x 5 cm x 4 cm x 6 cm
Volume of one triangular prism = 60 cm^3
Since there are two identical triangular prisms attached to the rectangular prism, we multiply the volume of one triangular prism by 2.
Volume of two triangular prisms = 60 cm^3 x 2 = 120 cm^3
Finally, we find the total volume of the composite figure by adding the volume of the rectangular prism and the volume of the two triangular prisms.
Total volume = Volume of rectangular prism + Volume of two triangular prisms
Total volume = 280 cm^3 + 120 cm^3
Total volume = 400 cm^3
Therefore, the volume of the composite figure is 400 cm^3.