10-5 Circles Course 1 Warm Up Problem of the Day Lesson Presentation

The perimeter is multiplied by 5, and the area is multiplied by 25. Course 1 10-5 Circles Warm Up The length and width of a rectangle are each multiplied by 5. Find how the perimeter and area of the rectangle change. The perimeter is multiplied by 5, and the area is multiplied by 25.

Circles 10-5 Problem of the Day Course 1 10-5 Circles Problem of the Day When using a calculator to find the height of a rectangle whose length one knew, a student accidentally multiplied by 20 when she should have divided by 20. The answer displayed was 520. What is the correct height? 1.3

Course 1 10-5 Circles Learn to identify the parts of a circle and to find the circumference and area of a circle.

Insert Lesson Title Here Course 1 10-5 Circles Insert Lesson Title Here Vocabulary circle center radius (radii) diameter circumference pi

Course 1 10-5 Circles A circle is the set of all points in a plane that are the same distance from a given point, called the center. Center

Course 1 10-5 Circles A line segment with one endpoint at the center of the circle and the other endpoint on the circle is a radius (plural: radii). Radius Center

Course 1 10-5 Circles A chord is a line segment with both endpoints on a circle. A diameter is a chord that passes through the center of the circle. The length of the diameter is twice the length of the radius. Radius Center Diameter

Additional Example 1: Naming Parts of a Circle Course 1 10-5 Circles Additional Example 1: Naming Parts of a Circle Name the circle, a diameter, and three radii. L Z M N The circle is circle Z. LM is a diameter. ZL, ZM, and ZN are radii.

Circles 10-5 Try This: Example 1 Course 1 10-5 Circles Try This: Example 1 Name the circle, a diameter, and three radii. G H D I The circle is circle D. IG is a diameter. DI, DG, and DH are radii.

Circles 10-5 The distance around a circle is called the circumference. Course 1 10-5 Circles The distance around a circle is called the circumference. Circumference Radius Center Diameter

Course 1 10-5 Circles The ratio of the circumference to the diameter, , is the same for any circle. This ratio is represented by the Greek letter , which is read “pi.” C d C d = 

Course 1 10-5 Circles The decimal representation of pi starts with 3.14159265 . . . and goes on forever without repeating. We estimate pi using either 3.14 or . 22 7 The formula for the circumference of a circle is C = d, or C = 2r.

Course 1 10-5 Circles Additional Example 2A: Using the Formula for the Circumference of a Circle Find the missing value to the nearest hundredth. Use 3.14 for pi. A. d = 11 ft; C = ? 11 ft C = d Write the formula. C  3.14 • 11 Replace  with 3.14 and d with 11. C  34.54 ft

Course 1 10-5 Circles Additional Example 2B: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. B. r = 5 cm; C = ? 5 cm C = 2r Write the formula. C  2 • 3.14 • 5 Replace  with 3.14 and r with 5. C  31.4 cm

Course 1 10-5 Circles Additional Example 2C: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. C. C = 21.98 cm; d = ? C = d Write the formula. 21.98  3.14d Replace C with 21.98 and  with 3.14. 21.98 3.14d _______ 3.14 3.14  Divide both sides by 3.14. 7.00 cm  d

Circles 10-5 Try This: Example 2A Course 1 10-5 Circles Try This: Example 2A Find the missing value to the nearest hundredth. Use 3.14 for pi. A. d = 9 ft; C = ? 9 ft C = d Write the formula. C  3.14 • 9 Replace  with 3.14 and d with 9. C  28.26 ft

Circles 10-5 Try This: Example 2B Course 1 10-5 Circles Try This: Example 2B Find each missing value to the nearest hundredth. Use 3.14 for pi. B. r = 6 cm; C = ? 6 cm C = 2r Write the formula. C  2 • 3.14 • 6 Replace  with 3.14 and r with 6. C  37.68 cm

Circles 10-5 Try This: Example 2C Course 1 10-5 Circles Try This: Example 2C Find each missing value to the nearest hundredth. Use 3.14 for pi. C. C = 18.84 cm; d = ? C = d Write the formula. 18.84  3.14d Replace C with 18.84 and  with 3.14. 18.84 3.14d _______ 3.14 3.14  Divide both sides by 3.14. 6.00 cm  d

Course 1 10-5 Circles The formula for the area of a circle is A = r2.

Additional Example 3: Using the Formula for the Area of a Circle Course 1 10-5 Circles Additional Example 3: Using the Formula for the Area of a Circle Find the area of the circle. Use for pi. d = 42 cm; A = ? 22 7 42 cm A = r2 Write the formula to find the area. r = d ÷ 2 The length of the diameter is twice the length of the radius. r = 42 ÷ 2 = 21 A  • 212 22 7 Replace  with and r with 21. 22 7 __ A  • 441 22 7 __ 63 Use the GCF to simplify. 1 A  1,386 cm2 Multiply.

Circles 10-5 Try This: Example 3 Course 1 10-5 Circles Try This: Example 3 Find the area of the circle. Use for pi. d = 28 cm; A = ? 22 7 28 cm A = r2 Write the formula to find the area. r = d ÷ 2 The length of the diameter is twice the length of the radius. r = 28 ÷ 2 = 14 A  • 142 22 7 Replace  with and r with 14. 22 7 __ A  • 196 22 7 __ 28 Use the GCF to simplify. 1 A  616 cm2 Multiply.

Insert Lesson Title Here Course 1 10-5 Circles Insert Lesson Title Here Lesson Quiz Find the circumference and area of each circle. Use 3.14 for . 1. 2. 3. Find the area of a circle with a diameter of 20 feet. Use 3.14 for . 3 in. 8 in. C = 25.12 in. C = 18.84 in. A = 50.24 in2 A = 28.26 in2 314 ft2