# EXPLORING CIRCUMFERENCE

A circle is a set of points in a plane that are a fixed distance from the center.

A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle. The length of a radius is called the radius of the circle.

A diameter of a circle is a line segment that passes through the center of the circle and whose endpoints lie on the circle. The length of the diameter is twice the length of the radius. The length of a diameter is called the diameter of the circle.

The circumference of a circle is the distance around the circle.

The above explained points have been illustrated in the diagram given below.

## Finding circumference

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)  =  2πr

The two equivalent formulas for circumference are C = πd and C = 2πr.

Example :

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.

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