Figuring Volume in a Cylinder

A solid cylinder and the volume equation.

Geometry can be tricky, especially trying to remember the multitude of formulas and methods to determine the volume of three-dimensional shapes. This step-by-step process should help you in determining the volume of a cylinder.

Things You'll Need

• Paper
• Pencil
• Calculator (optional)

Instructions

1. 

   Draw a sketch of the solid cylinder similar to that in the image.

2. 

   Determine what information you have about the cylinder. To find the volume, it is essential that you have the radius of the cylinder and the height. The radius is the distance from the center of the cylinder to the outer edge.Some word problems may make the problem more complex by giving you the diameter of the cylinder. To find the radius, just divide the diameter in half. Make certain that the units of the height and radius are the same (everything in centimeters or everything in inches). Convert if necessary.

3. 

   Write out the formula as shown in the image. V = Volumeh = Heightr = RadiusTake a moment to think what the formula means. The first part, (Pi)*r^2, is the formula for the area of a circle. Then multiply the area of the circle on the top of the cylinder by the height of the cylinder. This is the definition of volume: Area x Height. Remember, if you don't have a calculator, Pi is approximately 3.14.

4. 

   Use the information you have in the formula. It is easiest to do the formula in two parts, find the area first and then multiply it by the height.As an example, imagine a cylinder with a radius of 5 cm and a height of 20 cm. The area of the circle would be Pi multiplied by 5 cm squared (25), which is approximately 78.5 cm.

5. 

   Multiply the radius of the circle by the height of the cylinder as shown in the image. In our example, the resulting volume was 1570 cubic cm.