VIDEO: Calculate the circumference of a sphere

Necessary measurements on the sphere

If you want to determine the circumference of spheres, it depends on which measuring instruments you have available and how big the spheres are. If the size is suitable, you can measure the circumference directly with a thread or a tape measure, for example:

• In the case of small balls of the same type - such as lead shot - the best way to measure the volume is to use a certain number of balls fill a measuring cylinder in which, for example, exactly 100 cm³ of water are. Now add 100 balls and watch how much the water level rises, for example to 125 ml. Then you know that the spheres have a volume of 25 cm³, so a sphere has a volume of 0.25 cm³.
• You can also measure larger balls through perforated metal sheets, provided the diameter of the holes is known. If you have holes of a known diameter that are getting bigger and bigger in millimeter increments, then try out which hole the ball just falls through.
• Usually the diameter of a sphere is measured with a calliper. Hold the ball between the measuring jaws and push the movable jaw towards the stationary one until the ball is clamped between them. Be careful not to squeeze a soft ball while doing this. Read off the diameter of the sphere.
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Now all you need to determine the circumference is the relationship between the diameter and the diameter. Volume and scope.

Calculate the circumference

• If you have the diameter, it's easy because the circumference of a sphere is a circle. For circles, U = pi d applies. If the calculator doesn't have a key with pi, then take the approximate 3.14.
• If you have the volume it is a little more complicated because then you have to work out the diameter. The volume of a sphere is determined using the formula V = (1/6) pi d³. So if you know the volume, you need to multiply that by 6 and divide by pi. Now you have to take the third root of the obtained value. Then you have the diameter of the sphere. You can now calculate the diameter and insert it into the formula for the circumference U = pi d.

Alternatively, you can use the diameter d = ³Insert W (6V / pi) in the formula for the circumference. You then get the generally valid form U = pi ³W (6V / pi) after you have made the denominator rational by expanding with pi² and from pi³ have taken the third root in the denominator, you get U = ³W (6V pi²). Annotation: ³W is the third root. This can also be written as a fractional exponent, then the formula U = pi (6V pi²)^1/3 ring.