Area of sector

Transcript

Area of sector A sector is a section of the circle, like a slice of pizza Since sector is a part of the circle Area of sector is a fraction of the circle area Area of sector = 𝝅𝒓^𝟐 × 𝜽/(𝟑𝟔𝟎° ) Here, angle is measured in degrees Let’s do some examples Find Area of a semicircle A semicircle is half a circle Semicircle subtends 180° at the center ∴ 𝜃 = 180° Let Radius = r Now, Area of semicircle = 𝜋𝑟^2 × 𝜃/(360° ) = 𝝅𝒓^𝟐 × (𝟏𝟖𝟎° )/(𝟑𝟔𝟎° ) = 𝜋𝑟^2 × 1/2 = (𝝅𝒓^𝟐)/𝟐 Find length of a qudrant A quadrant is 𝟏/𝟒 a circle Semicircle subtends 90° at the center ∴ 𝜃 = 90° Let Radius = r Now, Area of quadrant = 𝜋𝑟^2 × 𝜃/(360° ) = 𝝅𝒓^𝟐 × (𝟗𝟎° )/(𝟑𝟔𝟎° ) = 𝜋𝑟^2 × 1/4 = (𝝅𝒓^𝟐)/𝟒