Worked Example: Basic Area and Volume
This worked example demonstrates how to calculate a 2D surface area and use that result to compute a 3D volume.
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This worked example demonstrates how to calculate a 2D surface area and use that result to compute a 3D volume.
A rectangular concrete water tank has an internal width of 2.0 meters and a length of 5.0 meters. If the tank is filled with water to a depth of 3.0 meters, calculate the cross-sectional base area and the total volume of water in the tank.
Base Area (2D): The area of a rectangle is the product of its width and length.
Volume (3D): The volume of a rectangular prism is the product of its base area and its height.
Understanding how 2D geometries sweep through a third dimension to create volume is fundamental in fluid mechanics, structural material estimation, and thermodynamics. In this example, the 30.0 cubic meters of volume directly translates to the capacity of the tank.
First, we calculate the area of the tank's base:
Next, we use the base area to calculate the total volume: