The image depicts a three-dimensional geometric figure, which appears to be a composite shape made of rectangular prisms. The dimensions given are 16 inches, 8 inches, 10 inches, and three instances of 7 inches, which likely correspond to the lengths, widths, and heights of different parts of the figure. The shape may be used in a mathematical context to calculate properties such as surface area or volume. What is the volume of the composite figure?
To find the volume of the composite figure, we need to first determine the volumes of the individual rectangular prisms and then add them together.
The first rectangular prism has dimensions 16 inches, 8 inches, and 10 inches. Therefore, its volume is:
Volume = length x width x height
Volume = 16 inches x 8 inches x 10 inches
Volume = 1280 cubic inches
The second rectangular prism has dimensions 7 inches, 7 inches, and 10 inches. Therefore, its volume is:
Volume = length x width x height
Volume = 7 inches x 7 inches x 10 inches
Volume = 490 cubic inches
The third rectangular prism also has dimensions 7 inches, 7 inches, and 10 inches. Therefore, its volume is:
Volume = length x width x height
Volume = 7 inches x 7 inches x 10 inches
Volume = 490 cubic inches
Now, we add up the volumes of all three rectangular prisms:
1280 cubic inches + 490 cubic inches + 490 cubic inches = 2260 cubic inches
Therefore, the volume of the composite figure is 2260 cubic inches.