Arc Length and Sector Area

Pre-Algebra · Axiom Academy

LESSON Arc Length and Sector Area A pie slice is just a fraction of the whole circle — and that one fraction sets both the curved crust and the slice's area. 1. A Slice Is a Fraction of the Circle A full turn is . A sector with central angle is exactly the fraction of the whole circle. Watch the wedge sweep open — the bar on the right tracks what fraction of the circle it has covered, the instant it covers it. The wedge's share of the whole turn 2. Arc Length Is That Fraction of the Circumference The whole way around is the circumference, . An arc is just the part of that edge the wedge covers — the fraction of it. The animation lifts the arc off the circle and unrolls it against the full circumference bar, so you can see it land on exactly its share. Find the arc length of a sector in a circle of radius . The angle is of the circle, and . 3. Sector Area Is That Fraction of the Area The same logic covers area. The whole disk has area ; a sector is the fraction of that filled-in space. The animation splits the disk into equal wedges and fills the chosen one, while a matching bar fills the same fraction of the total area — the wedge and the bar reach their share together. Find the sector area of a sector in a circle of radius . The angle is of the circle, and . At 3:00 the hour hand has swept , a quarter of the face; at 6:00 it has swept , half the circle. A category that is of the data takes the sector . To turn a percent into degrees, multiply by 3.6 .

This is the written version of the interactive lesson above. See the full Pre-Algebra course.