How to Calculate the Volume of a Conical Paper Cup

By Mark Kennan
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The volume of a cone is a measurement of the space inside the cone. For a paper cup, the volume measures the amount of liquid that the cup can hold. Knowing the volume will help you know much you are drinking. To find the volume of a conical paper cup, you need to know the height and diameter of the cup.

Step 1

Measure the height of the paper cup.

Step 2

Measure the diameter of the paper cup. The diameter is the distance across the circle, through the center.

Step 3

Divide the diameter by two to calculate the radius. For example, if the diameter is 3 inches, the radius would be 1.5 inches.

Step 4

Square the radius. For example, 1.5 squared is 2.25 square inches.

Step 5

Multiply the result from Step 4 by the height times pi (round to 3.14) times 1/3 to find the volume. For example, if the height is 3 inches, you would multiply 2.25 by 3.14 by 3 by 1/3 and find the volume to be 7.065 cubic inches.

About the Author

Mark Kennan is a writer based in the Kansas City area, specializing in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."