If the circumference of a circle is 100 units, then what will be the length of the arc described by an angle of 20 degrees?

### Concept & Proportionality The arc length corresponding to a specific central angle is simply that fraction of the total circumference. $$Arc\ Length = \frac{\theta}{360^\circ} \times Circumference$$ ### Step-by-Step Solution * Given total circumference, $C = 100$ units. * Given angle, $\theta = 20^\circ$. * Apply the proportional relationship: $Arc\ Length = \frac{20}{360} \times 100$ * Simplify the fraction: $\frac{20}{360} = \frac{1}{18}$ * Calculate the final value: $Arc\ Length = \frac{100}{18} = \frac{50}{9}$ * Convert to decimal: $\frac{50}{9} = 5.555...$ units. ### Exam Strategy & Shortcut Recognize that $20^\circ$ is exactly $\frac{1}{18}$ of a full $360^\circ$ circle. So you just need to divide the total circumference by $18$. Since $100/20$ would be $5$, $100/18$ must be slightly higher than $5$. The repeating decimal $\frac{50}{9} = 5.55...$ makes option (a) the obvious choice. ### Common Pitfall A common mistake is unnecessarily trying to calculate the radius first using $100 = 2\pi r$, and then plugging it back into the arc length formula. This wastes time and introduces rounding errors with $\pi$. ### Final Answer Therefore, the correct answer is **5.55 units**.