WarmUp Exercises Find the area of a circle

Warm-Up Exercises Find the area of a circle with the given measure. 1. Radius: 8 cm ANSWER about 201. 06 cm 2 2. Radius: 1 1 mi 3 ANSWER about 5. 59 mi 2

Warm-Up Exercises Find the area of a circle with the given measure. 3. Circumference: 4π ft ANSWER 4π ft 2 4. Solve x 2 = 100 π. ANSWER _ 5. 64 about +

Use the formula for area of a circle Warm-Up 1 Exercises EXAMPLE Find the indicated measure. SOLUTION A = πr 2 a. Area 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. r = 2. 5 cm ANSWER The area of A is about 19. 63 square centimeters.

Use the formula for area of a circle Warm-Up 1 Exercises EXAMPLE Find the indicated measure. SOLUTION A b. = πr 2 Write formula for the area of a circle. 113. 1 = πr 2 Substitute 113. 1 for A. 113. 1 = r 2 π 6 ≈ r ANSWER Diameter Divide each side by π. Find the positive square root of each side. A = 113. 1 cm 2 The radius is about 6 cm, so the diameter is about 12 centimeters.

Find areas of sectors Warm-Up 2 Exercises EXAMPLE 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°, m. UV = 70° and m. USV = 360° – 70° = 290°.

Find areas of sectors Warm-Up 2 Exercises EXAMPLE STEP 2 Find the areas of the small and large sectors. Area of small sector = m. UV° 360 ° 70 = 360° ≈ 39. 10 πr 2 π Write formula for area of a sector. 82 Substitute. Use a calculator.

Find areas of sectors Warm-Up 2 Exercises EXAMPLE 2 Area of large sector = m. USV πr 360° ° 290 = π ° 360 ≈ 161. 97 Write formula for area of a sector. 82 Substitute. Use a calculator. ANSWER The areas of the small and large sectors are about 39. 10 square units and 161. 97 square units, respectively.

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Use the diagram to find the indicated measure. 1. Area of ANSWER D about 615. 75 ft 2

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Use the diagram to find the indicated measure. 2. Area of red sector ANSWER about 205. 25 ft 2

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Use the diagram to find the indicated measure. 3. Area of blue sector ANSWER about 410. 50 ft 2.

Use the Area of a Sector Theorem Warm-Up 3 Exercises EXAMPLE Use the diagram to find the area of V. SOLUTION Area of sector TVU = m. TU° 360 Area of V Write formula for 40° 35 = 360° Area of V Substitute. 315 = Area of a sector. V ANSWER The area of V is 315 square meters. Solve for Area of V.

Standardized Test Practice Warm-Up 4 Exercises EXAMPLE 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.

Standardized Test Practice Warm-Up 4 Exercises EXAMPLE = ° 180 36(26) – 360° (π = 936 – [32π + 256] ≈ 579. 47 The area is about 579 square feet. ANSWER The correct answer is C. 82 ) + 162

Warm-Up Exercises GUIDED PRACTICE 4. Find the area of ANSWER for Examples 3 and 4 H. about 907. 92 cm 2

Warm-Up Exercises GUIDED PRACTICE 5. for Examples 3 and 4 Find the area of the figure. ANSWER about 43. 74 m 2

Warm-Up Exercises GUIDED PRACTICE 6. for Examples 3 and 4 If you know the area and radius of a sector of a circle, can you find the measure of the intercepted arc? Explain. ANSWER Yes; the formula for the area of sector is m π r 2 and if you solve this for m, you get A= 360 A. π r 2

Warm-Up Exercises Daily Homework Quiz 1. Find the area of the sectors formed by DEF. ANSWER 106. 03 in. 2, 141. 31 in. 2

Warm-Up Exercises Daily Homework Quiz 2. Use the area of the sector to find the area of R ANSWER 211. 09 cm 2

Warm-Up Exercises Daily Homework Quiz 3. Find the area of the shaded region. ANSWER 23. 18 ft 2