Circumference of a Circle

Math 10-3 Ch.3 Measurement

Properties of Circles…

 Yesterday we talked about the perimeter of various 3 sided and 4 sided shapes. How do we find the perimeter of a circle?

 First, let’s review the properties of the circle:  *All the points on a circle are equidistant (the same distance) from the CENTER of the circle.

Properties of Circles…

 *A line that passes through the center of a circle and touches the edge of the circle on both sides is called the diameter.

Properties of Circles…

 *A line that starts at the center of the circle and touches an outside edge is called the radius.

Diameter and Radius…

 *The radius can be calculated by dividing the diameter by 2

r d

2  *The diameter can be calculated by multiplying the radius by 2

d

 2

r

 *The circumference of a circle is the perimeter of the circle. It can be calculated with the formula :

C

 

d

 Where ◦ ◦ = “pi” a constant that is 3.14159….

◦ d = diameter

Ex1. What is the circumference of a circle with a diameter of 8 cm?

  C = ?

d= 8cm

C

 

d

  C = 3.14 x 8

*note: we will use the estimation of 3.14 for pi in this course

 = 25.12 cm

Ex2. What is the circumference of a circle with a radius of 2.5 mm?

      C = ?

d= ?

r = 2.5 mm *first we must find the diameter of the circle. d = 2 x r d= 2 x 2.5 mm = 5 mm

Ex2. What is the circumference of a circle with a radius of 2.5 mm?

C

 

d

  = 3.14 x 5  = 15.7 mm

Ex3. The circumference of a circle is 52cm. What is the diameter?

  C = 52 cm d = ?

C

 

d

 *We must perform opposite operations (algebra!) to calculate the diameter!

  First, fill in the formula with what we know: 52 cm = 3.14 x d    What is opposite of multiplying by 3.14? Dividing by 3.14 on

the other side!

 d = ~16.56 cm