The circumference of a circle is the distance around the circle.
The ratio of the circumference to the diameter is the same for all circles.
This ratio is called π or pi, and you can approximate it as 3.14 or as . You can use π to find a formula for circumference.
For any circle, C/d = π. Solve the equation for C to give an equation for the circumference of a circle in terms of the diameter.
The ratio of the circumference to the diameter is π.
C/d = π
Multiply both sides by d.
(C/d) x d = π x d
C = πd
The diameter of a circle is twice the radius. You can use the equation C = πd to find a formula for the circumference C in terms of the radius r.
C = π(2r)
C = 2πr
The two equivalent formulas for circumference are
C = πd and C = 2πr
Example 1 :
An irrigation sprinkler waters a circular region with a radius of 14 feet. Find the circumference of the region watered by the sprinkler. Use 22/7 for π.
Solution :
Use the formula.
C = 2πr
Plug 14 for r
C = 2π(14)
Plug 22/7 for π
C ≈ 2 x (22/7) x 14
Simplify
C ≈ 2 x (22/1) x 2
C ≈ 88
So, the circumference of the region watered by the sprinkler is about 88 feet.
Example 2 :
The diameter of a car wheel is 21 inches. Find the circumference of the wheel.
Solution :
Radius = Diameter / 2
Radius = 21/2 inches
Use the formula.
C = 2πr
Plug 21/2 for r
C = 2π(21/2)
Plug 22/7 for π
C ≈ 2 x (22/7) x (21/2)
Simplify
C ≈ 2 x (11/1) x (3/1)
C ≈ 66
So, the circumference of the wheel is 66 inches.
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