Problem Solution
Assuming the spool is a cylinder and the circumference we're winding around is that of a circle with the given area, we can write the relation between circumference and area as
... C = 2√(πA)
10 times the circumference is then
... 10C = 20√(π·20 cm²) = 40√(5π) cm ≈ 159 cm
Formula Derivation
The usual formulas for circumference and area are
... C = 2πr
... A = πr²
If we multiply the area formula by π and take the square root, we get
... πA = (πr)²
... √(πA) = πr
Multiplying this by 2 gives circumference.
... C = 2√(πA) = 2πr