1. Ms. Cuervo CAHSEE Prep CIRCUMFERENCE

2. Circumference 7MG 1.2 Students will use pi to find the circumference and diameter of circles. VOCABULARY Circumference: The distance around a circle Diameter: A line segment connecting two points on a circle and passing through the the center of the circle – the diameter is twice the length of the radius Radius – the radius is half the length of the diameter What is a circle? Click here to watch VIDEO!VIDEO!

3. DO NOW In your gym class, you have been collecting data on balls used in different sports. You have measured the distance around the balls and the distance across them. Your assignment is to determine the relationship between the two measurements. Divide the distance around each ball by the distance across it, and place your answer in the space provided. Type of BallDistance Around the Ball (C) Distance Across the Ball (d) Ratio of Distance Around to Distance Across (C ÷ d) Baseball9.42 in3.0 in Kickball18.84 in.6.0 in Soccer Ball26.69 in8.5 in Basketball29.83 in9.5 in 3.14 What do you notice about the ratios? Pi = Circumference ÷ diameter

5. Pi = circumference ÷ diameter When pi is written out as a decimal, the digits following the decimal point are endless. We use the approximations 3.14 and 22/7 for the value of pi. If you know the diameter of a circle, how can pi help you find the circumference? Pi × diameter = circumference If pi = c ÷ d, then C = pi x d If pi = c ÷ d, then C = pi x d

6. Circumference The distance around a circle is called the circumference. Circumference is similar to perimeter (distance around a shape). Perimeter describes the distance around a polygon. Circumference describes the distance around a circle. The distance across a circle has a special name: the diameter. The radius is half the diameter. Circumference = pi × diameter C = pi × d What is circumference? Click here to watch VIDEO!VIDEO

7. How do you find the circumference of a circle if you have the diameter? Click here to watch VIDEO!VIDEO The diameter of the clock is 18 inches. What is the circumference of the circle?

8. C = pi x d C = (3.14) x 18 in. C = 56.52 in.

9. You marry a rich man and he buys you a hot tub. After years of use, the tiling around the rim of the tub needs to be replaced. You need to determine the circumference of the tub in order to purchase the correct amount of tiles. You know that the radius is 3 feet. What is the circumference? How do you find the circumference of a circle if you have the radius? Click here to watch VIDEO!VIDEO

10. What is the radius of the hot tub? What is the diameter of the hot tub? How can you find the circumference if you know the diameter? What is the approximate value of pi? What is the approximate circumference of the hot tub? 3 feet 6 feet C = pi × d 3.14 or 22/7 C = pi x d C = (3.14) x 6 C = 18.84 feet

11. The button on your favorite coat fell off and you want to replace it with a new button. You know the circumference of the button is 6.28 centimeters. What is the diameter of the button? What information is given? What is the approximate diameter of the button?

12. How can we solve for the diameter? C = pi x d -Instead of solving for c, you need to solve for d. 6.28 = 3.14 x d -Substitute the values provided (circumference and pi) 6.28 = 3.14d 3.14 3.14 -Divide by 3.14 to solve for d. d = 2

13. Exit Slip Find the circumference.