# Circumference Formula

The circumference formula is used to calculate the distance around a circle.

Circumference formulas:

*C = 2πr* or *C = πd*

r is the radius and d is the diameter.

The diameter is the longest chord that runs through the center of the circle. The radius is the measure of the distance from the center of the circle to a point on the circle. The diameter is 2 times the measure of the radius. If we want an exact answer, we use π. If we want to approximate, we use 3.14.

Example 1:

Find the circumference of a circle with a radius of 5 centimeters.

Step 1:

Find variables necessary.

Radius, r = 5cm

Step 2:

Substitute into formula and multiply.

C = 2πr

C = 2π(5)

C = 10π

**Exact Answer:**

The circumference is 10π centimeters.

For an approximate answer, substitute 3.14 for π.

$C\approx 10\cdot 3.14\approx 31.4$

**Approximate answer:**

The circumference is about 31.4 centimeters.

Example 2:

Find the circumference of a circle with a diameter of 16 inches.

Step 1:

Find the variables

d=16

Since diameter is given, we will use the second formula.

Step 2:

Substitute.

C = πd

C = π . 16 = 16π

**Exact answer:**

The circumference is 16π inches.

$C\approx 16\cdot 3.14\approx 50.24$

**Approximate answer:**

The circumference is about 50.24 inches.

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