Post on 31-Dec-2015
transcript
Take a circle . . .
Divide it up into sectors
Colour the top semicircle green & the lower semicircle yellow
Pull the sectors apart
Arrange the green sectors in one line& the yellow sectors in another line
The sectors fit together like teeth . .
The sectors fit together like teeth . .
The sectors fit together like teeth . .
The sectors fit together like teeth . .
Think about the lengths involved . .
?
?
The “vertical” one is easy . . .
r
?
It’s the radius!
The other is . . .
r
?
Half the circumference
Remember the formula for the circumference . . .
r
?
Circumference 2 r
So, half the circumference is . . .
r
?
2
2
rr
So, we have . . .
r
r
But this shape is almost a rectangle . . .
r
r
So can you approximate its area?
The area is approximately
r
r
2Area r r
r
Now, think . . .
r
rWhat would happen if you cut the circle
into smaller and smaller sectors?
It would become even more like a rectangle . . .
r
rSo this approximation for the
area of the circle would be even more accurate . . .
So the area of a circle is . . .
2r