# Circles

If you divide the circumference of any circle by its diameter you will always get the same number 3.14...

This number is called pi. Pi is usually represented by the symbol π

Pi is an irrational number, that means it goes on forever, the first 50 digits of pi are: 3.14159265358979323846264338327950288419716939937510

To calculate the circumference of a circle we use the formula:
Circumference = π × diameter

This can be simplified to: Circumference = πd

Because 2 radiuses are equal to a diameter we can also use the formula:
Circumference = 2 × π × radius

This can be simplified to: Circumference = 2πr

It doesn't matter which formula you use, they are the same and will give the same answer.

Example 1: A circle has a diameter of 8 cm. Work out the circumference of the circle.

We can use the formula:
Circumference = π × diameter

We can substitute 8 in for the diameter:
Circumference = π × 8
π × 8 can be written as 8π

The diameter was given in cm, so the answer is 8π cm

We can leave the answer in terms of pi unless we are asked to give the answer as a decimal.

To convert our answer in to a decimal we can use a calculator, there should be a pi button on your calculator.

On the classwiz it is above the Ans button:

For the pi button we press shift then Ans:

=

To work out the circumference in the calculator we press:

This gives an answer of 8π, to convert the answer to a decimal we press the SD button:

This gives us 25.13274123, or 25.1 to 1 decimal place.

We can say the circumference is 25.1 cm to 1 decimal place.

Example 2: A circle has a radius of 9 metres. Work out the circumference of the circle.

This time we have been given the radius of a circle. We can either use the formula:
Circumference = 2 × π × radius

Or we could multiply the radius by 2 to get the diameter and use the formula:
Circumference = π × diameter

If we use:
Circumference = 2 × π × radius

We need to substitute 9 in for the radius:
Circumference = 2 × π × 9

If we are leaving our answer in terms of pi we can simplify our answer by multiplying 2 and 9
2 × 9 = 18
So now we have 18 × π which we can write as 18π

The radius was measured in metres so the answer is 18π metres

If we use a calculator to convert 18π to a decimal we get 56.5 metres to one decimal place.

Try these:

Find the circumference of this circle, give your answer to 1 decimal place:

Find the circumference of this circle, give your answer to 1 decimal place:

To calculate the area of a circle we use the formula:
Area = πr2

Example 3: A circle has a radius of 5.2 cm
Calculate the area of the circle.

To find the area of a circle we use the formula:
Area = πr2

We need to substitute 5.2 in for r:
Area = π(5.2)2

We can now type this into a calculator which gives us the answer of:
67625π

The radius was given in cm, and we measure area in squares, so the answer is:
67625π cm2

The calculator will convert the answer to a decimal if we press the SD button
As a decimal the answer is 84.9 cm2 to 1 decimal place

Example 4: A circle has a diameter of 9 cm
Calculate the area of the circle.

To find the area of a circle we use the formula:
Area = πr2

We can find the radius of the circle by halving the diameter:
92 = 4.5

We now need to substitute 4.5 in for r:
Area = π(4.5)2

We can now type this into a calculator which gives us the answer of:
814π

In terms of pi the answer is:
814π cm2

As a decimal the answer is 63.6 cm2 to 1 decimal place

Try these: