Formula to Find the Volume of a Cylinder

Cylinders are three-dimensional shapes that have two circles as bases and are connected by parallel lines to enclose the space between them. The volume of the cylinder is the empty space enclosed by the cylinder. All volume formulas are reported in units cubed, such as cubic inches or cubic feet because they represent three dimensions. Soup cans, oil barrels and silos are examples of cylinders.

  1. Formula for Volume of a Cylinder

    • The volume of a cylinder is found using the following equation where \"V\" is the volume, \"?\" is pi, estimated at 3.14, \"R\" is the radius and \"H\" is the height.
      V = ? R^2 H
      For example, if you had a cylinder with a radius of 8 inches and a height of 13 inches, your volume would be 2612.48 cubic inches.

    Explanation of the Formula

    • Three dimensional objects with straight edges have three measurements: length, width and height. The length and width multiplied give the area of the base. Then multiply by the height to get the volume. A cylinder does not have a length and a width because the base is a circle. However, you can substitute the area of the circle, which is found by multiplying ? by the radius squared, for length times width when finding the area of the base. Then multiply by the height to determine volume.

    Uses for Cylinder Volume

    • The formula for cylinder volume has several real word applications. If you were building a cylindrical silo to hold your grain each year after harvest, you would need to determine how much it could hold. For example, if you knew you needed to hold at least 100,000 square feet of wheat and you couldn't build your silo higher than 100 feet tall, you would know the radius would have to be 318.47 feet.

      If you wanted to find out how much you could fit into a soup can with a radius of 2 inches and a height of 4 inches, you would use the formula to find that there is 50.24 cubic inches of space inside.

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