Area of a Circle

1
Area of a Circle

• p

2
Starter

• Which of these shapes has the greatest perimeter?
  Which has the smallest?
• What is each perimeter in terms of d?

3
Starter Answer

• Square has 4 sides of length d 4d
• Hexagon has 6 sides of ½d 3d

4
Starter Answer

• Square has 4 sides of length d 4d
• Hexagon has 6 sides of ½d 3d

• Circle is between 3d and 4d pd

5
Areas

• Which of these shapes has the greatest area?
  Which has the smallest?
• What is the area in terms of r?

6
Areas

• Large square is 2r x 2r 4r2
• Small square is half of this 2r2

7
Areas

• Large square is 2r x 2r 4r2
• Small square is half of this 2r2

• Circle has area in between 2r2 and 4r2

8
Area of a circle

• A circle has radius r

9
Rearrange the sectors
10
Consider the lengths
So the length of this side is pr
Circumference of circle 2pr Length of half
circumference pr
11
Consider the lengths
So the height is r
pr
Radius of circle r
12
Consider the area
r
pr
Area of shape is close to area of parallelogram
base x height pr x r pr2
Hence the area of a circle is pr2
13
Summary

• A circle has radius rand diameter d
• Circumference of a circle C pd or C 2pr
• Area of a circle A pr2

Fiddle-dee-dum, fiddle-dee-dee A ring round the
moon is p times d But if you want a hole
repaired Then what you need is pr2.