Solution Procedure
Considering the spool as a cylindrical shape, and calculating the circumference based on the area cited, we establish the connection between circumference and area as follows:
... C = 2√(πA)
To find ten times this circumference, we calculate:
... 10C = 20√(π·20 cm²) = 40√(5π) cm ≈ 159 cm
Derivation of Formulas
The standard formulas for circumference and area are:
... C = 2πr
... A = πr²
Multiplying the area formula by π and extracting the square root yields:
... πA = (πr)²
... √(πA) = πr
Doubling this value results in the circumference formula:
... C = 2√(πA) = 2πr
