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
The volume of a rectangular prism is given by V = l * w * h.
Given:
Length = 14 cm
Width = 5 cm
Height = 4 cm
Volume of rectangular prism = 14 * 5 * 4 = 280 cm^3
The volume of a triangular prism is given by V = 1/2 * b * h * H, where b is the base length, h is the height, and H is the perpendicular distance between the bases.
Given:
Base length = 5 cm
Height = 6 cm
Perpendicular distance = 4 cm
Volume of one triangular prism = 1/2 * 5 * 6 * 4 = 60 cm^3
Since there are two identical triangular prisms attached to the rectangular prism:
Total volume of triangular prisms = 2 * 60 = 120 cm^3
Therefore, the total volume of the composite figure is 280 + 120 = 400 cm^3.
154 cm^3 is not an option and 616 cm^3, 952 cm^3, and 448 cm^3 are also not correct, so the volume of the composite figure is 400 cm^3.
WRONG PICK ONE OF THE OPTIONS OF448 cm3
448 cm cubed
952 cm3
952 cm cubed
616 cm3
616 cm cubed
154 cm3
Apologies for the error in my previous response.
The correct volume of the composite figure is:
Volume of the rectangular prism = 14 cm * 5 cm * 4 cm = 280 cm^3
Volume of two identical triangular prisms = 2 * (1/2 * 5 cm * 6 cm * 4 cm) = 2 * 60 cm^3 = 120 cm^3
Total volume = 280 cm^3 (rectangular prism) + 120 cm^3 (two triangular prisms) = 400 cm^3
Given the options provided, the closest one is 448 cm^3. The closest one among the options is:
448 cm^3.