Areas of Circles and Sectors

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Areas of Circles and Sectors

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Presentation transcript:

Areas of Circles and Sectors 6.8 Areas of Circles and Sectors Theorem 6.20: Area of a Circle The area of a circle is p times the square of the radius. r

Areas of Circles and Sectors 6.8 Areas of Circles and Sectors Example 1 Use the formula for area of a circle Find the indicated measure. Area Solution Write formula for area of a circle. Substitute ____ for r. Simplify. Use a calculator.

Areas of Circles and Sectors 6.8 Areas of Circles and Sectors Example 1 Use the formula for area of a circle Find the indicated measure. Area Diameter Solution Write formula for area of a circle. Substitute _____ for A. Divide each side by ___. Find the positive sq. rt. of each side. The radius is about ___ inches, so the diameter is about ___ inches

Areas of Circles and Sectors 6.8 Areas of Circles and Sectors Theorem 6.21: Area of a Sector The ratio of the area of a sector of a circle to the area of the whole circle (pr2) is equal to the ratio of the measure of the intercepted arc to 360o. P A B r

Areas of Circles and Sectors 6.8 Areas of Circles and Sectors Q R S P Example 2 Find areas of sectors Find the area of the sector formed by Solution Step 1 Find the measure of the minor and major arcs.

Areas of Circles and Sectors 6.8 Areas of Circles and Sectors Q R S P Example 2 Find areas of sectors Find the area of the sector formed by Solution Step 2 Find the areas of the small and large sectors. Area of small sector =

Areas of Circles and Sectors 6.8 Areas of Circles and Sectors Q R S P Example 2 Find areas of sectors Find the area of the sector formed by Solution Step 2 Find the areas of the small and large sectors. Area of large sector = The areas of the small and large sectors are about _______ square units and _______ square units, respectively.

Areas of Circles and Sectors 6.8 Areas of Circles and Sectors Example 3 Use the Area of a Sector Theorem C A B Use the diagram to find the area of . Solution . Area of sector ACB = . . . The area of is ______ square meters.

Areas of Circles and Sectors 6.8 Areas of Circles and Sectors Checkpoint. Complete the following exercise. Find the radius of the circle.

Areas of Circles and Sectors 6.8 Areas of Circles and Sectors Checkpoint. Complete the following exercise. Find the areas of the sectors formed by P R S Q Area of small sector = Area of large sector =

Areas of Circles and Sectors 6.8 Areas of Circles and Sectors Checkpoint. Complete the following exercise. . Find the area of F H G . Area of sector FGH = . .

Circumference and Arc Length 6.7 Circumference and Arc Length Pg. 242, 6.8 #1-22