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.
Incorrect, choose a different answer.
No, it's something other than 700.
To find the volume of the composite figure, we first need to find the volume of each individual prism.
Volume of rectangular prism = length x width x height
Volume = 14 cm x 5 cm x 4 cm = 280 cubic cm
Volume of triangular prism = (1/2) x base x height x length
Volume = (1/2) x 5 cm x 6 cm x 14 cm = 210 cubic cm (for each triangular prism)
Since there are two identical triangular prisms, the total volume contributed by the triangular prisms is 2 x 210 = 420 cubic cm.
Therefore, the total volume of the composite figure is the sum of the volumes of the rectangular prism and the two triangular prisms:
Total volume = 280 cubic cm + 420 cubic cm = 700 cubic cm
So, the volume of the composite figure is 700 cubic cm.
I apologize for the error in my previous calculation.
To find the volume of the composite figure, we consider the rectangular prism and the two identical triangular prisms separately.
Volume of rectangular prism = length x width x height = 14 cm x 5 cm x 4 cm = 280 cubic cm
Volume of each triangular prism = (1/2) x base x height x length = (1/2) x 5 cm x 6 cm x 14 cm = 210 cubic cm
Since there are two identical triangular prisms, the total volume contributed by the triangular prisms is 2 x 210 = 420 cubic cm.
The total volume of the composite figure is the sum of the volumes of the rectangular prism and the two triangular prisms:
Total volume = 280 cubic cm + 420 cubic cm = 700 cubic cm
Therefore, the volume of the composite figure is 700 cubic cm.
Let's revisit the calculation for the volume of the composite figure.
The volume of the rectangular prism = length x width x height = 14 cm x 5 cm x 4 cm = 280 cubic cm
The volume of each triangular prism = (1/2) x base x height x length = (1/2) x 5 cm x 6 cm x 14 cm = 210 cubic cm
Since there are two identical triangular prisms, the total volume contributed by the triangular prisms is 2 x 210 = 420 cubic cm.
The total volume of the composite figure is the sum of the volumes of the rectangular prism and the two triangular prisms:
Total volume = 280 cubic cm (rectangular prism) + 420 cubic cm (two triangular prisms) = 700 cubic cm
Therefore, the correct volume of the composite figure is indeed 700 cubic cm.