9-5 Area of Circles Warm Up Problem of the Day Lesson Presentation Course 2 Warm Up Problem of the Day Lesson Presentation
9-5 Area of Circles Warm Up Simplify. 1. 82 2. 122 3. 6.22 64 4. 7.52 Course 2 9-5 Area of Circles Warm Up Simplify. 1. 82 2. 122 3. 6.22 4. 7.52 64 144 38.44 56.25
9-5 Area of Circles Problem of the Day Course 2 9-5 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 9-5 Area of Circles Learn to find the area of circles.
9-5 Area of Circles So the area of the parallelogram can be written as Course 2 9-5 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 = 2r, A = (2r)r = r2.
• 9-5 Area of Circles AREA OF A CIRCLE A = r2 Course 2 9-5 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 9-5 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 = 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 9-5 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 . 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.
9-5 Area of Circles Check It Out: Example 1A Course 2 9-5 Area of Circles Check It Out: Example 1A Find the area of the circle to the nearest tenth. Use 3.14 for . 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.
9-5 Area of Circles Check It Out: Example 1B Course 2 9-5 Area of Circles Check It Out: Example 1B Find the area of the circle to the nearest tenth. Use 3.14 for . 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 9-5 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.
9-5 Area of Circles Check It Out: Example 2 Course 2 9-5 Area of Circles Check It Out: 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 9-5 Area of Circles Additional Example 3: Application Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. 1.5 cm The measurement of the radius of the circle is 1.5 cm. Now find the area of the entire circle. A = r2 Use the formula for the area of a circle. A = 3.14 · 1.52 Substitute. Use 1.5 for r. A 3.14 · 2.25 Evaluate the power. A 7.07 Multiply.
Additional Example 3 Continued Course 2 9-5 Area of Circles Additional Example 3 Continued Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. Since of the circle is shaded, divide the area of the circle by 2. 7.07 ÷ 2 = 3.535. 1 2 The area of the shaded region of the circle is about 3.5 cm2.
9-5 Area of Circles Check It Out: Example 3 Course 2 9-5 Area of Circles Check It Out: Example 3 Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. 2.4 cm The measurement of the radius of the circle is 2.4 cm. Now find the area of the entire circle. A = r2 Use the formula for the area of a circle. A = 3.14 · 2.42 Substitute. Use 2.4 for r. A 3.14 · 5.76 Evaluate the power. A 18.09 Multiply.
Check It Out: Example 3 Continued Course 2 9-5 Area of Circles Check It Out: Example 3 Continued Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. Since of the circle is shaded, divide the area of the circle by 4 and subtract the answer from the entire area. 18.0864 ÷ 4 = 4.52. 18.0864 – 4.52 = 13.56. 3 4 The area of the shaded region of the circle is about 13.56 cm2.
Insert Lesson Title Here Course 2 9-5 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