How to Calculate the Perimeter of a Cylinder

You can measure the perimeter of a silo without measuring all the way around it.

The perimeter of a cylinder is essentially the circumference of its circular cross section. Remember the circumference of a circle is 2*pi*radius. Here, pi is the ratio of circumference to diameter for all circles, a constant with never-ending digits equal to 3.14159 (after rounding). You can easily find the perimeter of a cylinder, given other measurements. Denote the cylinder height by H, circumference by C, radius by R, volume by V and cross-sectional area by A. Useful formulas are that the cross-sectional area of the cylinder is pi*R^2 and its volume is the cross-sectional area times the height. ^2 means here that the radius, R, is squared.

Things You'll Need

• 2 metersticks or yardsticks

Instructions

1. Calculate the circumference of a cylinder, given the radius, R, or diameter, D, by multiplying by pi. Specifically, double R to get D. Then multiply by pi.

   For example, if the radius is 1 meter, multiply by 2 to get a diameter of 2 meters. Then multiply by pi to get 6.28 meters in circumference (after rounding).

2. Calculate the circumference of a cylinder, given the volume, V, and the height, H, by dividing V by H to get the cross-sectional area, A. Divide A by pi and take the square root to get the radius, R. Then double the radius and multiply by pi.

   In equations, V=AH. So V/H = A. A = pi*R^2, so the square root of A/pi is R. The circumference, C, is 2*pi*R.

   For example, if V = 5 meters-cubed and H = 1 meter, then A = (5 meters-cubed) / (1 meter) = 5 meters-squared. The radius is the square root of 5/pi meters, or 1.59 meters, after rounding. So the circumference, C, is 2*pi*R = 10 meters.

3. Find the circumference of a large cylindrical structure, such as a silo, by first measuring the structure's curvature. Specifically, take a meterstick or yardstick, and place one end on the side of the cylinder, holding the stick horizontal and tangential to the point of contact. Hold a second meter- or yardstick horizontally, perpendicular to the end of the first stick, to measure the distance the cylinder is away from the end of the first stick. Denote the length of the first stick X and the second distance measured Y. You are effectively measuring how fast the cylinder "drops away" or curves away from a tangential line. Now calculate pi*(Y+X/Y) to solve for the circumference.

   For example, if a meter stick with one end touching the side of a silo tangentially has its other end one meter away from the silo when measured with a stick adjacent to the first, then the circumference is pi*(1+1/1) = 2pi. This makes sense, since the two sticks are at a right angle with each other and the radius of the cross-sectional circle must be one meter.

References

• Israel Science and Technology Page: Formulas for Geometrical Figures
• 1728: Circle Formulas