How to Calculate the Capacity of a Cylinder

Written by w d adkins
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A cylinder is one of the basic geometric solid forms of the curvilinear type. To understand what this means, think of a soup or paint can. A cylinder consists of the cylindrical surface (the side of the can) bounded by ends that are circular and at right angles to the side (the top and bottom of the can). A cylinder can be a solid or hollow object. Suppose you want to know the capacity of a cylinder that is hollow. The capacity is defined by the volume. Once you find the volume, you've found the capacity of the cylinder.

Skill level:
Moderately Easy

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Things you need

  • Calculator
  • Tape measure
  • Empty can or other cylinder

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Instructions

  1. 1

    Know the formula for the capacity of a cylinder. Basically, it's the area of an end multiplied by the height of the cylinder (we'll label the height "h"). Since the end is a circle, it's area is given by Pr^2, where P = pi (which is 3.1416) and "r" is the radius of the circle. So the basic equation for the volume ("V") of a cylinder is V = hPr^2.

  2. 2

    Measure the height of the cylinder. Next, carefully find the circumference of the cylinder. You can do this by wrapping a measuring tape around the can at one end and line up the tape so it's exactly at the end all the way around.

  3. 3

    Calculate the radius of the cylinder. First, find the diameter of the cylinder by dividing the circumference by 3.1416 (value of pi). For example, if the circumference is 18.85cm, the diameter is 6cm. The radius is equal to half the diameter (or 3cm).

  4. 4

    Find the volume of the cylinder. Once you have the height and the radius of the cylinder, this is a straightforward multiplication exercise from Step 1, V = hPr^2. Let's assume you measured the height ("h") at 20cm. Plugging in the numbers from the previous steps, we get V = 20cm times (3cm)^2 times 3.1416, or 578.232 cubic cm. That's the capacity of the cylinder.

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