# The circumference of a circle worksheet. Using Pi and the diameter to find the perimeter.

The perimeter of a circle is known as the circumference of the circle (the distance around the circle). If you have the diameter of the circle (the distance across the centre) then the circumference (C) is found by the following formula:

**C = πd**

Alternatively, you can use the formula C = 2πr as the diameter is twice the radius. However, in the examples that follow, the first formula shall be used. Also, the symbol π represents Pi, which is a mathematical constant equal to 3.14 (to 2 decimal places). It’s best to use the Pi button on your scientific calculator in the examples that follow.

Example 1

Work out the circumference of a circle of diameter 5 yards.

So if you have remembered the formula above then all you need to do is multiply the diameter of 5 by Pi:

C = πd

= π × 5

= 15.7 yards to 1 decimal place

Example 2

The rim of a cup has a diameter of 2 inches. Work out the circumference of the cup to 1 decimal place.

So all you need to do is plug in the diameter of 2 inches into the above formula:

C = πd

= π × 2

= 6.3 inches to 1 decimal place

Example 3

A large circular window has a radius of 3.5 feet. Work out the circumference of the window to 1 decimal place.

This time the question gives you the radius of the circle. So you need to double this value to give the diameter:

2 × 3.5 = 7 feet.

So the diameter of the window is 7 feet which you can now plug into C = πd.

C = πd

= π × 7

= 22.0 feet to 1 decimal place.

Example 4

The circumference of a circle is 50m. Work out the diameter of the circle to 1 decimal place.

This time you are calculating the diameter from the circumference, so you will need to make the diameter the subject of the formula. Since Pi is multiplied by d, then divide both sides of the formula by Pi:

C = πd (divide by π)

C/ π = d

**d = C/ π**

Now that d is the subject of the formula, then all you need to do is substitute C = 50 into this formula:

d = 50/π

d = 15.9m to 1 decimal place.

So working out the circumference of a circle is actually quite easy to do as you just need to multiply the diameter by Pi. Make sure that you memorise the formula C = πd and don’t mix it up with other formulas involving Pi such as the area of a circle (A = πr²).

## Circle Help

- How to work out the arc length and perimeter of a se...

If you take a part of the circumference of a circle then the distance along this arc is called the arc length. So since the arc length is part of the circumference of a circle, then the arc length of the sector can be found by using the following... - Area of a semicircle. Finding the area of semi circl...

To find the area of a semicircle first you need to find the area of the whole circle and divide your answer by 2, as a semicircle takes up half the space of a circle. To find the area of the circle use... - Area of a semicircle. Finding the area of semi circl...

To find the area of a semicircle first you need to find the area of the whole circle and divide your answer by 2, as a semicircle takes up half the space of a circle. To find the area of the circle use...

## More by this Author

- 0
The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if...

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...

- 26
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple...