Area of sectors

Learning Objectives Define a sector of a circle and identify its key components: the central angle and the radius. Derive the formula for the area of a sector as a fraction of the area of a full circle. Calculate the area of a sector given the radius and the central angle in degrees. Calculate the area of a sector given the radius and the central angle in radians. Solve for a missing radius or central angle when the area of the sector is known. Apply the area of a sector formula to solve real-world problems. Ever wondered how much pizza you're actually getting in one slice? 🍕 That's a question about the area of a sector! This tutorial will guide you through the concept of a sector, which is simply a 'slice' of a circle. You will learn the formulas to ca...

TermDefinitionExample CircleA two-dimensional shape consisting of all points in a plane that are at a given distance from a given point, the center.A bicycle wheel is a physical representation of a circle. Radius (r)A straight line segment from the center of a circle to any point on its circumference.If a pizza has a diameter of 14 inches, its radius is 7 inches. Central Angle (θ)An angle whose vertex is the center of a circle and whose sides are two radii intersecting the circle at two points.If you cut a pizza into 8 equal slices, the central angle of each slice is 360° / 8 = 45°. SectorThe region of a circle enclosed by two radii and the arc between them, resembling a slice of a pie.A single slice of a round cake is a sector of the whole cake. Degrees (°)A common unit of measurement fo...

Area of a Circle A = \pi r^2 This is the foundational formula for the area of a full circle, where 'r' is the radius. The area of a sector is always a fraction of this total area. Area of a Sector (Angle in Degrees) A_{sector} = \frac{\theta}{360} \times \pi r^2 Use this formula when the central angle (θ) is given in degrees. It represents the fraction of the circle (θ/360) multiplied by the total area. Area of a Sector (Angle in Radians) A_{sector} = \frac{1}{2} r^2 \theta Use this formula when the central angle (θ) is given in radians. It is a more direct formula often used in higher-level mathematics.