Area of a Circle

π

Starter• Which of these shapes has the greatest

perimeter? Which has the smallest?

• What is each perimeter in terms of d?

d d d

Starter Answer

• Square has 4 sides of length d 4d

• Hexagon has 6 sides of ½d3d d d d

½d

½d

Starter Answer

• Square has 4 sides of length d 4d• Hexagon has 6 sides of ½d 3d • Circle is between 3d and 4d πd

Areas

• Which of these shapes has the greatest area? Which has the smallest?

• What is the area in terms of r? r r r

Areas

• Large square is 2r x 2r = 4r2

• Small square is half of this = 2r2

r r r 2r

Areas

• Large square is 2r x 2r = 4r2

• Small square is half of this = 2r2

• Circle has area in between 2r2 and 4r2

Area of a circle

• A circle has radius r

Rearrange the sectors

Consider the lengths

Circumference of circle = 2πr

Length of half circumference = πr

So the length of this side is πr

Consider the lengths

Radius of circle = r

So the height is r

πr

Consider the area

Area of shape is close to area of parallelogram = base x height

= πr x r= πr2

r

πr

Hence the area of a circle is = πr2

Summary• A circle has radius r

and diameter d

• Circumference of a circle C = πd or C = 2πr

• Area of a circle A = πr2

r

d

Fiddle-dee-dum, fiddle-dee-dee

A ring round the moon is π times d

But if you want a hole repaired

Then what you need is πr2.