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.
A. 952cm
B. 448cm
C. 154cm
D. 616cm
To find the volume of the composite figure, we 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 = 14cm x 5cm x 4cm
Volume of rectangular prism = 280cm
Volume of triangular prism = 1/2 x base x height x length
Volume of each triangular prism = 1/2 x 5cm x 6cm x 14cm
Volume of each triangular prism = 210cm
Since there are two identical triangular prisms, the total volume of both is 210cm + 210cm = 420cm
Therefore, the volume of the composite figure is 280cm + 420cm = 700cm
So, the correct answer is not provided in the options. The volume of the composite figure is 700cm.
A. 952cm
B. 448cm
C. 154cm
D. 616cm
To find the volume of the composite figure, let's calculate the volume of each individual shape:
1. Volume of rectangular prism:
Length = 14cm, Width = 5cm, Height = 4cm
Volume = Length x Width x Height
Volume = 14cm x 5cm x 4cm
Volume = 280cm
2. Volume of each triangular prism:
Base = 5cm, Height = 6cm, Length = 14cm
Volume = 0.5 x Base x Height x Length
Volume = 0.5 x 5cm x 6cm x 14cm
Volume = 210cm
Since there are 2 identical triangular prisms attached on either side of the rectangular prism, the total volume contributed by the 2 triangular prisms will be:
2 x 210cm = 420cm
Total volume of the composite figure:
Rectangular prism volume + Triangular prism volume
280cm + 420cm = 700cm
The correct answer is not provided in the options. The volume of the composite figure is 700cm, and none of the options provided match this value.