9-8 Circles and Circumference Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

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. Course Circles and Circumference

Problem of the Day When using a calculator to find the width 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 width? 1.3 Course Circles and Circumference

Learn to identify the parts of a circle and to find the circumference of a circle. Course Circles and Circumference

Vocabulary circle center radius (radii) diameter circumference pi Insert Lesson Title Here Course Circles and Circumference

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 Circles and Circumference

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

A diameter is a line segment that passes through the center of the circle and has both endpoints on the circle. The length of the diameter is twice the length of the radius. Center Radius Diameter Course Circles and Circumference

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

Check It Out: Example 1 Name the circle, a diameter, and three radii. The circle is circle D. IG is a diameter.DI, DG, and DH are radii. G H D I Course Circles and Circumference

The distance around a circle is called the circumference. Center Radius Diameter Circumference Course Circles and Circumference

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 Circles and Circumference

The decimal representation of pi starts with and goes on forever without repeating. We estimate pi using either 3.14 or Course Circles and Circumference

Formula to find the circumference of a circle: C =  d (d is the diameter) Or C= 2  r (r is the radius) USE 3.14 for . Course Circles and Circumference

Additional Example 2: Application A skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding  to 3. C =  dC  3 8C  24 ft Write the formula. Replace  with 3 and d with 8. 8 ft Course Circles and Circumference

Check It Out: Example 2 A second skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding  to 3. C = dC  3 14C  42 yd Write the formula. Replace  with 3 and d with yd Course Circles and Circumference

Additional Example 3A: Using the Formula for the Circumference of a Circle Find the missing value to the nearest hundredth. Use 3.14 for pi. d = 11 ft; C = ? C = dC  C  ft Write the formula. Replace  with 3.14 and d with ft Course Circles and Circumference

Additional Example 3B: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. r = 5 cm; C = ? C = 2rC  C  31.4 cm Write the formula. Replace  with 3.14 and r with 5. 5 cm Course Circles and Circumference

Additional Example 3C: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. C = cm; d = ? C = d  3.14d7.00 cm  d Write the formula. Replace C with and  with d _______  Divide both sides by Course Circles and Circumference

Check It Out: Example 3A Find the missing value to the nearest hundredth. Use 3.14 for pi. d = 9 ft; C = ? C = dC  C  ft Write the formula. Replace  with 3.14 and d with 9. 9 ft Course Circles and Circumference

Check It Out: Example 3B Find each missing value to the nearest hundredth. Use 3.14 for pi. r = 6 cm; C = ? C = 2rC  C  cm Write the formula. Replace  with 3.14 and r with 6. 6 cm Course Circles and Circumference

Check It Out: Example 3C Find each missing value to the nearest hundredth. Use 3.14 for pi. C = cm; d = ? C = d  3.14d6.00 cm  d Write the formula. Replace C with and  with d _______  Divide both sides by Course Circles and Circumference

Lesson Quiz Find the circumference of each circle. Use 3.14 for  Find the circumference of a circle with diameter of 20 feet. Use 3.14 for . C = in. Insert Lesson Title Here C = in. 8 in ft 3 in. Course Circles and Circumference