1. Circles: Circumference What do we call the measure of the perimeter of a circle or the distance around a circle? circumference

2. Circles: Circumference The parts of the circle: diameter radius center The circle A

3. Circles: Circumference 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).

4. Circles: Circumference 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 the radius, use formula #1; when the problem gives the diameter use formula #2.

5. Circles: Circumference 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

6. Circles: Circumference 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.

7. Circles: Circumference 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.

8. Circles: Circumference How Do I Find It? 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 ≈ 81.64 in. d = 2r = 2 x 13 = 26 in.

9. Circles: Area What is area? Does this definition apply to the area of a circle? Explain. What is the formula for finding area of a circle? Area is the number of unit squares it takes to cover a figure. Yes. Even though squares cannot fit perfectly into a circle, you can approximate the partial squares or you can find the area using a formula.

10. Circles: Area What kind of units did we get when we found the circumference of a circle? What kind of units do we get when we find the area of a circle? Why are these units different? We find square units such as sq. cm, sq. in, sq. ft, sq. mi, etc. We found one- dimensional units such as cm, in, ft, mi, etc. Circumference is a one-dimensional measurement (length only) and area is a two- dimensional measurement (length and width; base and height; radius and radius)

11. Circles: Area A portion of each circle is covered by a square. The length of a side of the shaded square is the same length as the radius of the circle. We call such a square a “radius square”. Circle 1 Circle 3 Circle 2

12. Circles: Area How many radius squares does it take to cover each circle? Let’s explore further to answer this question. Circle 1 Circle 3 Circle 2

13. Circles: Area How can you find the area of a circle if you know the radius? How can you find the radius of a circle if you know the area? Multiply the radius squared times pi( π ). Divide the area by 3.14 to get the area of the radius square. Then find the square root of the area of the radius square.

14. Circles: Area 1.Find the area of a circle that has a radius of 2.5 cm. 2.Find the area of a circle that has a diameter of 14 cm. A = π r ≈ 3.14 x 2.5 cm x 2.5 cm ≈ 9.625 cm 2 2 d = 2r A = π r r = 7 ≈ 3.14 x 7 cm x 7 cm ≈ 153.86 cm 2 2