University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

214

Pages:

2
Author:

albulaastediasjn4

Areas of Circles & Sectors Vocabulary Terms: Population Density: # of people / Area of the Land Sector of a circle: a portion of the circle area Core Concepts: Area of a Circle: The area of a circle is A = πr² where r is the radius of the circle. Area of a Sector: The ratio of the area of a sector of a circle to the area of the whole circle (πr²) is equal to the ratio of the measure of the intercepted arc to 360°. Area of sector APB = (m∠APB/360) * πr² Extra Practice Exercises 1-2: Find the indicated measure. Area of OM A = πr² d = 2r 5 = 2r r = 2.5 A = π(2.5)² A = 6.25π cm² Area of OR A = πr² A = π(7)² A = 49π m² Exercises 3-8: Find the indicated measure. Area of a circle with a diameter of 1.8 inches d = 2r 1.8 = 2r r = 0.9 A = πr² A = π(0.9)² A = 0.81π in² Diameter of a circle with an area of 10 square feet A = πr² 10 = πr² 10/π = r² r ≈ 1.7841 d = 2r d ≈ 2(1.7841) d ≈ 3.5682 Radius of a circle with an area of 65 square centimeters A = πr² 65 = πr² 65/π = r² r ≈ 4.5486 cm Area of a circle with a radius of 6.1 yards A = πr² A = π(6.1)² A = 37.21π yd² Areas of the sectors formed by ∠PQR Sector = degree/360 * (πr²) = 140/360 * (π4²) = 56π/9 cm² Area of OY Sector = degree/360 * (πr²) = 255/360 * (π4.1²) = 59.04 ft² Problem 9: About 70,000 people live in a region with a 30-mile radius. Find the population density in people per square mile. Area of land = πr² = π(30)² = 900π Population density = # of people / Area of land = 70,000 / 900π ≈ 24.7574 people per mile²