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8-2 FORMULAS

Understand the concepts of radius and diameter, circumference calculations, and area formulas for circles. Learn how to find arc length and sector areas using basic calculations.

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8-2 FORMULAS

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  1. 8-2 FORMULAS Area Circumference Sectors

  2. REVIEW: RADIUS AND DIAMETER • The RADIUS is the measure of any radius. • Radius is usually abbreviated as . • The DIAMETER is the measure of any diameter. • Diameter is usually abbreviated as . r d

  3. CIRCUMFERENCE: • The distance around the circle. • If you unwrap a circle, how long will the line be? or So what is anyway?

  4. Example: Find the Circumference of the Circle Exact Answer cm cm Approximate Answer

  5. AREA • The area of a region is the number of unit squares that can fit into the region (or the space inside the region.) • The area of a unit square = length X width = (1 cm) X (1 cm) = 1X1 X cm x cm = 1 cm2 For area the units are always squared! Unit Square

  6. AREA • The area of a circle is the number of unit squares that can fit into the circle. How many squares are in the circle? You can estimate by counting… Or use the formula!

  7. AREA FORMULA • The area of a circle with radius r is given by This gives us the EXACT number of squares! r (It’s usually not a whole number.)

  8. Example: Find the Area of the Circle Exact Answer • Find the area of the following circle. cm2 cm2 Approximate Answer

  9. Fraction of a Circle • What fraction of the whole circle is a given arc? • Find the measure of the central angle. • Divide by 360, the total number of degrees in the circle. 180º diameter This arc is one-half of a circle.

  10. Fraction of a Circle • What fraction of the whole circle is this arc? • Find the measure of the central angle. • Divide by 360, the total number of degrees in the circle. This arc is one-fifth of a circle.

  11. Fraction of a Circle • What fraction of the whole circle is this (major) arc? • Find the measure of the central angle. • The major arc measure is: 360º – minor arc measure = 360º - 140º = 220º • Divide by 360, the total number of degrees in the circle. 140º 220º This arc is eleven-eighteenths of a circle.

  12. Fraction of a Circle • What fraction of the whole circle is a given arc? • Find the measure of the central angle. • Divide by 360, the total number of degrees in the circle. a Fraction of the circle =

  13. Arc Length • The distance around an arc • The amount of crust on a slice of pizza. • The ratio of the center angle and 360° (the FRACTION OF THE CIRCLE) multiplied by the CIRCUMFERENCE

  14. Arc Length Formula Arc Length = (fraction of the circle) X (circumference) = fr x C = x2r = x2r

  15. Example: Find the Arc Length • A.L. (arc length) = fraction *circ. = Exact Answer (in terms of ) in in Approximate Answer (nearest tenth)

  16. SECTOR • sector of a circle - part of the interior of a circle bounded by two radii and an arc.

  17. AREA OF A SECTOR • The area of a sector of a circle • The size of a slice of pizza. • The FRACTION OF THE CIRCLE multiplied by the AREA OF THE CIRCLE.

  18. Area of a Sector Formula Area of a Sector = (fraction of the circle) X (area of circle) = fr x A = Xr2 = Xr2

  19. Example: Find the Area of the Sector • A.S. (area of a sector) = fraction *area 72° Exact Answer (in terms of ) in2 Approximate Answer (nearest tenth) in2

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