FINDING CIRCUMFERENCE OF A CIRCLE

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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