Area of sectors

Learning Objectives Define a sector of a circle and identify its key components. Understand that a sector represents a fractional part of a whole circle. Calculate the area of a whole circle given its radius using an approximation for pi. Determine the fraction of a circle represented by a given sector (e.g., from a description or central angle). Apply fraction multiplication to find the area of a sector from the area of the whole circle. Solve real-world problems involving the area of sectors. Ever wondered how much pizza you get in one slice? 🍕 That's a sector! Let's find out how big it really is! In this lesson, you'll learn what a sector is and how to calculate its area. This skill helps us understand parts of circles in everyday life, from food portions...

TermDefinitionExample CircleA round shape where all points on its edge are the same distance from a central point.A hula hoop or the face of a clock. RadiusThe distance from the center of a circle to any point on its edge.If a pizza is 10 inches across, its radius is 5 inches (half of the distance across). CenterThe exact middle point of a circle, from which all points on the edge are equally distant.The very middle of a dartboard. SectorA part of a circle enclosed by two radii and the curved edge (arc) between them, like a slice of pizza or pie.One slice cut from a round cake. Central AngleThe angle formed by the two radii of a sector at the center of the circle.A 90-degree angle for a quarter of a circle, or 180 degrees for a half-circle. AreaThe amount of surface inside a two-dimension...

Area of a Circle A = \pi r^2 To find the area (A) of a whole circle, multiply pi (\pi, approximately 3.14) by the radius (r) multiplied by itself (r squared). This gives you the total space inside the circle. Area of a Sector \text{Area of Sector} = (\text{Fraction of Circle}) \times (\text{Area of Circle}) To find the area of a sector, first determine what fraction of the whole circle the sector represents. This fraction can be found by dividing the sector's central angle by 360 degrees. Then, multiply this fraction by the total area of the circle.