Warm-up Inside Out Powerpoint Surrounding A Circle Guided Practice Finding Circumference Independent Practice How Do I Find It? Measurement

Inside Out (Warm Up) Find the perimeter and area of the trapezoid. 9 in. 5 in. 6 in in Perimeter = 26 in. 3 5 Area = 42 in.

Surrounding a Circle In previous lessons you found the perimeter of polygons. In today’s lesson you will find the perimeter of a circle. What do we call the measure of the perimeter of a circle or the distance around a circle? circumference

Surrounding a Circle Work with your partner to name the parts of the circle. diameter radius center The circle A

Surrounding a Circle Define the parts of a circle. Circle – Center – Diameter – Radius – A two-dimensional shape in which every point is the same distance from a point called the center. A point in a circle that is equidistant from every point on the circle. Circles are named by their center. Any line segment from a point on a circle through the center to another point on the circle. (d means diameter) Any line segment from the center of a circle to a point on the circle. (r means radius).

Surrounding a Circle Use your formula chart to find the two formulas for finding the circumference of a circle. Formula #1: ______________ Formula #2:_______________ How do we know when to use which formula? C = 2 π r C = π d When the problem gives you the radius use formula #1; when the problem gives you the diameter use formula #2.

Surrounding a Circle What are the decimal and fractional approximations for pi ( π )? How do we know which one to use? If the problem involves decimals use 3.14; if the problem involves fractions use. 22 7

Surrounding a Circle Can you find the circumference of a circle if you know its diameter? If so, how? Can you find the diameter of a circle if you know its circumference? If so, how? Yes. Multiply the diameter by 3.14 and that will give you the circumference. Yes. Divide the circumference by 3.14 and that will give you the diameter.

Surrounding a Circle What is the relationship between the diameter of a circle and the radius of the same circle? Can you find the circumference of a circle if you know its radius? If so, how? Can you find the radius of a circle if you know its circumference? Yes. Multiply the radius by 2 and then by 3.14 and that will give you the circumference. Yes. Divide the circumference by (2 x 3.14) and that will give you the radius. The diameter is twice the radius, or the radius is half the diameter.

Finding Circumference (Guided Practice) The teacher will provide you and your partner with a circular object to measure. Use a tape measure to measure the circumference and diameter of a circular object. Record the results of your object as well as the objects the rest of the class measured in a table with columns for the object, diameter, and circumference. ObjectDiameterCircumference Answers will vary.

Finding Circumference (Guided Practice cont.) Study your table. Look for patterns and relationships between the circumference and the diameter. What conclusion can you draw about this relationship? ObjectDiameterCircumference Answers will vary. Possible answer: They should see that the circumference divided by the diameter give you pi( π ).

Finding Circumference (Guided Practice, cont.) Use your graphing calculator to recreate your table in the list feature. Use a formula and calculate the relationship between the circumference and the diameter of any circle. Possible answer: The results of dividing the circumference by the diameter should give them ≈ ObjectDiameterCircumferenceRelationship Answers will vary.

How Do I Find It? (Independent Practice) 1.A soft-drink can is about 2 inches in diameter. What is its circumference? 2.A bicycle wheel has a radius of about 13 inches. Find its circumference. What is its diameter? C = π d ≈ 3.14 x 2 ≈ 6.28 in. C = 2 π r ≈ 2 x 3.14 x 13 ≈ in. d = 2r = 2 x 13 = 26 in.