EXAMPLE 1 Use the formula for area of a circle Find the indicated measure. a. Area r = 2.5 cm SOLUTION Write formula for the area of a circle. = π (2.5)

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Presentation transcript:

EXAMPLE 1 Use the formula for area of a circle Find the indicated measure. a. Area r = 2.5 cm SOLUTION Write formula for the area of a circle. = π (2.5) 2 Substitute 2.5 for r. = 6.25π Simplify. ≈ Use a calculator. A = πr 2 The area about square centimeters. ANSWER

EXAMPLE 1 Use the formula for area of a circle Find the indicated measure. A = cm 2 b. Diameter Write formula for the area of a circle. Substitute for A = πr 2 = r π Divide each side by π. 6 ≈ r Find the positive square root of each side. The radius is about 6 centimeters, so the diameter is about 12 centimeters. ANSWER A = πr 2 SOLUTION

EXAMPLE 2 Find areas of sectors Find the areas of the sectors formed by UTV. SOLUTION STEP 1 Find the measures of the minor and major arcs. Because m UTV = 70 °, mUV = 70 ° and mUSV = 360 ° – 70 ° = 290 °.

EXAMPLE 2 STEP 2 Find the areas of the small and large sectors. Area of small sector = πr 2 m UV 360 ° Write formula for area of a sector. = π ° 360 ° Substitute. ≈ Use a calculator. Find areas of sectors

EXAMPLE 2 = π ° 360 ° Substitute. ≈ Use a calculator. Find areas of sectors The areas of the small and large sectors are about square units and square units, respectively. ANSWER Area of large sector = πr 2 m USV 360 ° Write formula for area of a sector.

GUIDED PRACTICE for Examples 1 and 2 1. Area of D Use the diagram to find the indicated measure. SOLUTION A = πr 2 Write formula for the area of a circle. = π (14) 2 Substitute 14 for r. = 196π Simplify. = Use a calculator The area of D is about ft 2.

GUIDED PRACTICE for Examples 1 and 2 2. Area of red sector SOLUTION STEP 1 Find the measures of major arcs. Use the diagram to find the indicated measure. Because m FDE = 120, mFE = 120 and mFGE = 360 – 120 = 140.

GUIDED PRACTICE for Examples 1 and 2 Write formula for area of a sector. = π Substitute. = Use a calculator. Area of red sector = π r 2 m FE 360 The area of red sector is about ft 2. ANSWER STEP 2 Find the area of red sector.

GUIDED PRACTICE for Examples 1 and 2 3. Area of blue sector SOLUTION STEP 1 Find the measure of the blue arc. Because m FDE = 120, MFE = 120 and mFGE = 360 – 120 = 240. Use the diagram to find the indicated measure.

GUIDED PRACTICE for Examples 1 and 2 Area of blue sector = π r 2 m FEG 360 Write formula for area of a sector. = π Substitute. = ft 2 Use a calculator. Area of blue sector is about ft 2. ANSWER STEP 2 Find the area of blue sector.