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:

How to remember the circumference and area mnemonic

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 150m² but if the centre circle has a radius of 9 metres will one pack be enough?

Exam question of an example to measure the circumference of a circle

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	10m²	10m²	8m²
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.