How to Calculate the Cubic Volume of a Log

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A straight log might not be a perfect cylinder, but it's very close. That means that if you're being asked to find the volume of a log, you can use the formula for finding volume of a cylinder to make a very close approximation. But before you can use the formula, you also need to know the log's length and either its radius or its diameter.

TL;DR (Too Long; Didn't Read)

Apply the formula for volume of a cylinder, V = π × r2 × h, where V is the log's volume, r is the radius of the log and h is its height (or if you prefer, its length; the straight-line distance from one end of the log to the other).

  1. Convert Diameter to Radius

  2. If you already know the log's radius, skip straight to Step 2. But if you've measured or been given the log's diameter, you must first divide it by 2 to get the log's radius. For example, if you've been told that the log has a diameter of 1 foot, its radius would be:

    1 ft ÷ 2 = 0.5 ft

    Tips

    • Note that in this case, the radius could be expressed in either inches or feet. Leaving it in feet is a judgment call because the log's length is likely to be expressed in feet as well. Both measurements must use the same unit, or the formula won't work.

  3. Measure or Discover the Log's Length

  4. In order to work the formula for volume of a cylinder, you'll also need to know the cylinder's height, which for a log is really its length straight from one end to the other. For this example, let the log's length be 20 feet.

  5. Substitute Radius and Length Into the Formula

  6. The formula for volume of a cylinder is V = π × r2 × h, where V is the volume, r is the radius of the log and h is its height (or in this case, the length of the log). After substituting the radius and length of your example log into the formula, you have:

    V = π × (0.5)2 × 20

  7. Simplify the Equation

  8. Simplify the equation to find the volume, V. In most cases, you can substitute 3.14 for π, which gives you:

    V = 3.14 × (0.5 ft)2 × 20 ft

    Which simplifies to:

    V = 3.14 × 0.25 ft2 × 20 ft

    And this finally simplifies to:

    V = 15.7 ft3

    The volume of the example log is 15.7 ft3.

References

About the Author

Lisa studied mathematics at the University of Alaska, Anchorage, and spent several years tutoring high school and university students through scary -- but fun! -- math subjects like algebra and calculus.

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