what is the formula to estimate the amount of fabric that is on a 2" cardboard core?
Insufficient data. Is board 2" thick or 2" by 2"?
2" diameter cardboard core
If 2" = diameter, is it a sphere or cylinder? If it is a cylinder, you need the height.
If a sphere, the surface area is:
A = 4πr^2
If d = 2, then r = 1 and r^2 = 1, therefore:
A = 4π
To estimate the amount of fabric on a 2" cardboard core, you'll need to know the length of the fabric wound around the core. Here is how you can calculate it:
1. Measure the diameter of the fabric roll: If the cardboard core has a diameter of 2", then its radius would be 1" (since the radius is half of the diameter).
2. Determine the circumference of the cardboard core: The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. In this case, the circumference would be C = 2π(1) = 2π inches.
3. Measure the length of fabric on one full revolution: This can be done by rolling out the fabric from the core and measuring the distance it covers for one complete revolution around the core.
4. Multiply the length of fabric on one full revolution by the circumference of the core: Multiply the length of fabric on one full revolution by the calculated circumference of the core. The result will give you the estimate of the fabric on the given core.
For example, let's say the length of the fabric on one full revolution is 10 inches:
Estimated fabric amount = Length of fabric on one full revolution * Circumference of the core
= 10 inches * 2π inches
= 20π square inches (or approximately 62.8 square inches)
So, the estimated amount of fabric on the 2" cardboard core would be 20π square inches (or approximately 62.8 square inches).