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a. Area. = π (2.5) 2. r = 2.5 cm. ANSWER. The area about 19.63 square centimeters. Use the formula for area of a circle. EXAMPLE 1. Find the indicated measure. SOLUTION. A = π r 2. Write formula for the area of a circle. Substitute 2.5 for r. = 6.25π. Simplify. ≈ 19.63. - PowerPoint PPT Presentation
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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.
≈ 19.63 Use a calculator.
A = πr2
The area about 19.63 square centimeters.
ANSWER
EXAMPLE 1 Use the formula for area of a circle
Find the indicated measure.
A = 113.1 cm2
b. DiameterWrite formula for the area of a circle.
Substitute 113.1 for A.113.1 = πr2
= r2113.1π
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 = πr2
SOLUTION
EXAMPLE 2 Find areas of sectors
Find the areas of the sectors formed by UTV.
SOLUTION
STEP 1Find 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 = πr2
mUV360°
Write formula for area of a sector.
= π 8270°
360°Substitute.
≈ 39.10 Use a calculator.
Find areas of sectors
EXAMPLE 2
= π 82290°
360°Substitute.
≈ 161.97 Use a calculator.
Find areas of sectors
The areas of the small and large sectors are about 39.10 square units and 161.97 square units, respectively.
ANSWER
Area of large sector = πr2 mUSV360°
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 = πr2 Write formula for the area of a circle.
= π (14)2 Substitute 14 for r.
= 196π Simplify.
= 617.75 Use a calculator
The area of D is about 615.75 ft2.
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 142120360
Substitute.
= 205.25 Use a calculator.
Area of red sector = π r2
mFE360
The area of red sector is about 205.25 ft2.
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 r2
mFEG360
Write formula for area of a sector.
= π 142240360
Substitute.
= 410.50 ft2 Use a calculator.
Area of blue sector is about 410.50 ft2.
ANSWER
STEP 2
Find the area of blue sector.