To find the arc length of a semicircle, you can use a specific formula derived from the circumference of a full circle.
Here's how:
The arc length of a semicircle is calculated as half the circumference of a full circle. Given the formula for the circumference of a circle is 2πr (where 'r' is the radius), and a semicircle represents 180 degrees out of the circle's total 360 degrees, according to the provided reference, the arc length can be found using the formula: (2 π r) × 180°/360°.
Here's a breakdown:
- Circumference of a Full Circle: 2 π r
- Semicircle's Proportion: 180°/360° which simplifies to 1/2
- Arc Length of Semicircle: (2 π r) (1/2) which further simplifies to π r
In essence, the arc length of a semicircle is simply π times the radius (r).
