Chapter 9 Measurement;: Length And Area Worksheet Page 26
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MEASUREMENT: LENGTH AND AREA (Chapter 9)
F
THE AREA OF A CIRCLE
Consider cutting a circle of radius r into 16 equal sectors and arranging them as shown:
r
~ r
p * r
(half the circumference)
p *
circumference is 2 *
r
DEMO
The figure obtained closely resembles a rectangle.
Perform this
The height of the rectangle is the radius of the circle.
demonstration for
yourself by cutting
The top “edge” is the sum of all the arc lengths of
equal sectors from
the green sectors. This is half the circumference of
this protractor.
the circle, which is
PROTRACTOR
1
£ 2 £ ¼ £ r = ¼ £ r.
2
The bottom “edge” is made up from the arcs of the
yellow sectors in a similar way.
p
2 *
* r
If the original circle is cut into 1000
equal sectors and arranged in the
r
same way, the resulting figure is
indistinguishable from a rectangle.
p * r
So, the area of the circle A = length £ width of the rectangle
) A = ¼ £ r £ r
2
) A = ¼r
2
The area of a circle of radius r is given by Area = ¼r
.
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