# Remember the circumference and area of a circle formula

The circumference of a circle `=\pi\timesdiameter`

The area of a circle `=\pi\times\radius\times\radius`

Or `=\pi\times\radius^2`

So to remember these formula the following will help:

**NOTE:**

`Circumference=\pi\times\diameter`

Is the same as `Circumference=2\pir`

And then `Area=\pir^2`

**Example 1**

The grass in the centre circle of a school’s football pitch has died. The grounds keeper has seen they can buy a pack of grass seed that will cover an area of 150m^{2} but if the centre circle has a radius of 9 metres will one pack be enough?

**Answer:**

The area of a circle = `\pir^2`

Therefore the area of the centre circle `=\pi\times\9^2=\pi\times81=254.5m^2`

**Answer:**

One pack of grass seed will not be enough to reseed the centre circle of the football pitch.

**Example 2**

A council contractor has been asked to paint 20 mini roundabouts each with a diameter of 4m. The purchasing manager at the contractors contacts 3 suppliers to check prices stock levels and coverage per tin of paint as shown in the table below. From which supplier should the contractor purchase the paint?

Supplier |
Blimey No Quality |
Boys & Boden |
Terribly Pricey |

Cost per tin |
£5.00 |
£5.30 |
£5.10 |

Coverage per tin |
10m |
10m |
8m |

Tins in stock |
20 |
35 |
35 |

**Answer:**

Stage 1 - First work out the area to be covered by all the mini roundabouts

The area of a circle = `\pir^2`

Radius = half diameter so each mini roundabout has a radius = `4÷2 = 2m`

Therefore area of each mini roundabout = `\pi\times2^2 = 12.57m^2`

Total area of all roundabouts = `20times12.57=251.40m^2`

Stage 2 – Now work out how many tins would be required from each supplier to paint all the mini roundabouts.

Blimey No Quality

`251.4/10=25.14` Therefore 26 tins would be required

So this supplier does not have enough tins in stock to paint all the mini roundabouts.

Boys & Boden

`251.4/10=25.14` Therefore 26 tins would be required

Terribly Pricey

`251.4/8=231.43` Therefore 32 tins would be required

Stage 3 – Work out the cost for the required number of paint tins from the suppliers.

Boys & Boden

`26times£5.30=£137.80`

Terribly Pricey

`32times£5.10=£163.20`

**Answer:**

Therefore the contractor should purchase the paint for the mini roundabouts from Boys & Boden.

# Remember the circumference and area of a circle formula

The circumference of a circle `=\pi\timesdiameter`

The area of a circle `=\pi\times\radius\times\radius`

Or `=\pi\times\radius^2`

So to remember these formula the following will help:

**NOTE:**

`Circumference=\pi\times\diameter`

Is the same as `Circumference=2\pir`

And then `Area=\pir^2`

**Example 1**

The grass in the centre circle of a school’s football pitch has died. The grounds keeper has seen they can buy a pack of grass seed that will cover an area of 150m^{2} but if the centre circle has a radius of 9 metres will one pack be enough?

**Answer:**

The area of a circle = `\pir^2`

Therefore the area of the centre circle `=\pi\times\9^2=\pi\times81=254.5m^2`

**Answer:**

One pack of grass seed will not be enough to reseed the centre circle of the football pitch.

**Example 2**

A council contractor has been asked to paint 20 mini roundabouts each with a diameter of 4m. The purchasing manager at the contractors contacts 3 suppliers to check prices stock levels and coverage per tin of paint as shown in the table below. From which supplier should the contractor purchase the paint?

Supplier |
Blimey No Quality |
Boys & Boden |
Terribly Pricey |

Cost per tin |
£5.00 |
£5.30 |
£5.10 |

Coverage per tin |
10m |
10m |
8m |

Tins in stock |
20 |
35 |
35 |

**Answer:**

Stage 1 - First work out the area to be covered by all the mini roundabouts

The area of a circle = `\pir^2`

Radius = half diameter so each mini roundabout has a radius = `4÷2 = 2m`

Therefore area of each mini roundabout = `\pi\times2^2 = 12.57m^2`

Total area of all roundabouts = `20times12.57=251.40m^2`

Stage 2 – Now work out how many tins would be required from each supplier to paint all the mini roundabouts.

Blimey No Quality

`251.4/10=25.14` Therefore 26 tins would be required

So this supplier does not have enough tins in stock to paint all the mini roundabouts.

Boys & Boden

`251.4/10=25.14` Therefore 26 tins would be required

Terribly Pricey

`251.4/8=231.43` Therefore 32 tins would be required

Stage 3 – Work out the cost for the required number of paint tins from the suppliers.

Boys & Boden

`26times£5.30=£137.80`

Terribly Pricey

`32times£5.10=£163.20`

**Answer:**

Therefore the contractor should purchase the paint for the mini roundabouts from Boys & Boden.