Length of an Arc of a Circle

Transcript

Length of an Arc of a Circle For a circle with radius r Length of an arc = 𝟐𝝅𝒓 × 𝜽/(𝟑𝟔𝟎° ) We also write this as 𝒍=𝟐𝝅𝒓 × 𝜽/(𝟑𝟔𝟎° ) Let’s do some examples Find length of a semicircle A semicircle is half a circle Semicircle subtends 180° at the center ∴ 𝜃 = 180° Let Radius = r Now, Length of an arc = 2𝜋𝑟 × 𝜃/(360° ) = 𝟐𝝅𝒓 × (𝟏𝟖𝟎° )/(𝟑𝟔𝟎° ) = 2𝜋𝑟 × 1/2 = 𝝅𝒓 Find length of a qudrant A quadrant is 𝟏/𝟒 a circle Semicircle subtends 90° at the center ∴ 𝜃 = 90° Let Radius = r Now, Length of an arc = 2𝜋𝑟 × 𝜃/(360° ) = 𝟐𝝅𝒓 × (𝟗𝟎° )/(𝟑𝟔𝟎° ) = 2𝜋𝑟 × 1/4 = 𝝅𝒓/𝟐