Areas of Circles and Sectors Warm Up Lesson Presentation Lesson Quiz

Warm-Up Find the area of a circle with the given measure. 1. Radius: 8 cm ANSWER about 201.06 cm2 2. Radius: 1 3 mi ANSWER about 5.59 mi2

Warm-Up Find the area of a circle with the given measure. 3. Circumference: 4π ft ANSWER 4π ft2 4. Solve x2 = 100 π . ANSWER about _ + 5.64

Find the indicated measure. a. Area Example 1 Find the indicated measure. a. Area r = 2.5 cm SOLUTION A = πr2 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. The area of A is about 19.63 square centimeters.

Find the indicated measure. b. Diameter Example 1 Find the indicated measure. b. Diameter A = 113.1 cm2 SOLUTION A = πr2 Write formula for the area of a circle. 113.1 = πr2 Substitute 113.1 for A. = r2 113.1 π Divide each side by π. 6 ≈ r Find the positive square root of each side. The radius is about 6 cm, so the diameter is about 12 cm.

Example 2 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°.

Find the areas of the small and large sectors. Example 2 STEP 2 Find the areas of the small and large sectors. Area of small sector = πr2 mUV 360° Write formula for area of a sector. = π 82 70° 360° Substitute. ≈ 39.10 Use a calculator. Area of large sector = πr2 mUSV 360° Write formula for area of a sector. = π 82 290° 360° Substitute. ≈ 161.97 Use a calculator. The areas of the small and large sectors are about 39.10 square units and 161.97 square units, respectively.

Guided Practice Use the diagram to find the indicated measure. 1. Area of D about 615.75 ft2 ANSWER 2. Area of red sector about 205.25 ft2 ANSWER 3. Area of blue sector about 410.50 ft2. ANSWER

Use the diagram to find the area of V. Example 3 Use the diagram to find the area of V. SOLUTION Area of sector TVU = Area of V mTU 360° Write formula for area of a sector. 35 = Area of V 40° 360° Substitute. 315 = Area of V Solve for Area of V. The area of V is 315 square meters.

Example 4 SOLUTION The area you need to paint is the area of the rectangle minus the area of the entrance. The entrance can be divided into a semicircle and a square.

Example 4 180° = 36(26) – (π 82 ) + 162 360° = 936 – [32π + 256] ≈ 579.47 The area is about 579 square feet. The correct answer is C. ANSWER

Guided Practice 4. Find the area of H. about 907.92 cm2 ANSWER

Guided Practice 5. Find the area of the figure. about 43.74 m2 ANSWER

Guided Practice 6. If you know the area and radius of a sector of a circle, can you find the measure of the intercepted arc? Explain. Yes; the formula for the area of sector is m A = and if you solve this for m, you get 360 π r2 360A . ANSWER

Lesson Quiz 1. Find the area of the sectors formed by DEF. ANSWER 106.03 in.2, 148.44 in.2

Lesson Quiz 2. Use the area of the sector to find the area of R ANSWER 211.09 cm2

Lesson Quiz 3. Find the area of the shaded region. ANSWER 23.18 ft2