8-6 Area of Circles Warm Up Problem of the Day Lesson Presentation Course 2 Warm Up Problem of the Day Lesson Presentation

8-6 Area of Circles Warm Up Simplify. 1. 82 2. 122 3. 6.22 64 4. 7.52 Course 2 8-6 Area of Circles Warm Up Simplify. 1. 82 2. 122 3. 6.22 4. 7.52 64 144 38.44 56.25

8-6 Area of Circles Problem of the Day Course 2 8-6 Area of Circles Problem of the Day A 16 in. pizza sells for $11.99. A 10 in. pizza sells for $5.99. Which size gives you more pizza per penny? Explain. The larger pizza; you get more than twice as much (64 in2 instead of 25 in2) for about twice the price.

Course 2 8-6 Area of Circles Learn to find the area of circles.

Course 2 8-6 Area of Circles A circle can be cut into equal-sized sectors and arranged to resemble a parallelogram. The height h of the parallelogram is equal to the radius r of the circle, and the base b of the parallelogram is equal to one-half the circumference C of the circle. So the area of the parallelogram can be written as 1 2 A = bh, or A = Cr. 1 2 Since C = 2r, A = (2r)r = r2.

• 8-6 Area of Circles AREA OF A CIRCLE A = r2 Course 2 8-6 Area of Circles AREA OF A CIRCLE The area A of a circle is the product of  and the square of the circle’s radius r. A = r2 • r

Additional Example 1A: Finding the Area of a Circle Course 2 8-6 Area of Circles Additional Example 1A: Finding the Area of a Circle Find the area of the circle to the nearest tenth. Use 3.14 for . A. A = r2 Use the formula. 7 cm A  3.14 · 72 Substitute 7 for r. A  3.14 · 49 Evaluate the power. A  153.86 Multiply. The area of the circle is about 153.9 cm2. The order of operations calls for evaluating the exponents before multiplying. Remember!

Additional Example 1B: Finding the Area of a Circle Course 2 8-6 Area of Circles Additional Example 1B: Finding the Area of a Circle Find the area of the circle to the nearest tenth. Use 3.14 for . B. A = r2 Use the formula. 18 ft A  3.14 · 92 Substitute 9 for r. A  3.14 · 81 Evaluate the power. A  254.34 Multiply. The area of the circle is about 254.3 ft2.

8-6 Area of Circles Try This: Example 1A Course 2 8-6 Area of Circles Try This: Example 1A Find the area of the circle to the nearest tenth. Use 3.14 for . A. A = r2 Use the formula. 10 cm A  3.14 · 102 Substitute 10 for r. A  3.14 · 100 Evaluate the power. A  314 Multiply. The area of the circle is about 314 cm2.

8-6 Area of Circles Try This: Example 1B Course 2 8-6 Area of Circles Try This: Example 1B Find the area of the circle to the nearest tenth. Use 3.14 for . B. A = r2 Use the formula. 12 ft A  3.14 · 62 Substitute 6 for r. A  3.14 · 36 Evaluate the power. A  113.04 Multiply. The area of the circle is about 113.0 ft2.

Additional Example 2: Application Course 2 8-6 Area of Circles Additional Example 2: Application Park employees are fitting a top over a circular drain in the park. If the radius of the drain is 14 inches, what is the area of the top that will cover the drain? Use 22 7 for . A =  r2 Use the formula for the area of a circle. 22 7 A  ·142 Substitute. Use 14 for r. 28 22 7 A  · 196 Evaluate the power. 1 A  22 · 28 A  616 Multiply. The area of the top that will cover the drain is about 616 in2.

8-6 Area of Circles Try This: Example 2 Course 2 8-6 Area of Circles Try This: Example 2 Albert was designing a cover for a spa. If the radius of the spa is 7 ft, what is the area of the cover that will be made? Use 22 7 for . A =  r2 Use the formula for the area of a circle. 22 7 A  ·72 Substitute. Use 7 for r. 7 22 7 A  · 49 Evaluate the power. 1 A  22 · 7 A  154 Multiply. The area of the top that will cover spa is about 154 ft2.

Additional Example 3: Application Course 2 8-6 Area of Circles Additional Example 3: Application A golf course is irrigated with sprinklers that spray in a circle. If a sprinkler waters a circular area with a radius of 25 feet, how many square feet does the sprinkler cover? Round your answer to the nearest whole number. A =  r2 Use the formula for the area of a circle. A =  · 252 Substitute. Use 25 for r. A  1963.495408 Use a calculator.  25  x2 A  1,963 Round. The sprinkler covers about 1,963 ft2.

8-6 Area of Circles Try This: Example 3 Course 2 8-6 Area of Circles Try This: Example 3 Janet had a circular fish pond in her back yard. She wanted to find the surface area of the pond. If it had a radius of 13 feet, what is its surface area in square feet? Round your answer to the nearest whole number. A =  r2 Use the formula for the area of a circle. A =  · 132 Substitute. Use 13 for r. A  530.9216 Use a calculator.  13  x2 A  531 Round. The pond has a surface area of about 531 ft2.

Insert Lesson Title Here Course 2 8-6 Area of Circles Insert Lesson Title Here Lesson Quiz Find the area of each circle, to the nearest tenth. Use 3.14 for . 1. 3. The bull’s-eye on a target has a diameter of 2 in. What is the area of the bull’s-eye to the nearest tenth? Use 3.14 for . 4. A round table cloth has a radius of 36 in. What is the area of the table cloth? Use 3.14 for . Round your answer to the nearest tenth. 2. 9 ft 8 ft • • 201.0 ft2 63.6 ft2 3.1 in2 4,069.4 in2