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#### 你知道圆的面积计算公式是怎么来的吗

Area of a circle, how to get the formula.

πr^2 gives you the area of a circle

but where does πr^2 come from ?

first, we’ll draw circle and fill in it’s area

next we will divide it into large equal parts

and arrange them in a rectangular formation

as you can see it barely resembles a rectangle

so next we will divide the circle into small equal pieces

and we will arrange them in the same manner

you can see that it appears more like a rectangle

so if we divide the circle into even more smaller pieces

you can see that every time the shape becomes more like a rectangle

so how small must we divide a circle

before we can get a perfect rectangle?

well, we can keep on dividing the circle into small, smaller,

or the smallest pieces you can make

but the answer is to divide the circle infinitely many times

until we cannot distinguish the lines

and eventually the circle can now become a perfect rectangle

so the area of the circle

is equal to the area of the rectangle

which is equal to Base times Height

the height of the rectangle

As you can see is the same as the radius

so height is equal to radius

to find the base

we need to look at the circumference of the circle

and when we compared the base and the circumference

we can see that the base is equal to

one-half the circumference

remember that the circumference is equal to 2πr

when we combine it with one-half

the two’s cancel out

and base is equal to πr

so now base times height becomes πr times r

combine the r’s together and we have πr^2

which is equal to the area of the rectangle

which is equal to the area of the circle

so πr^2 can be used to calculate

the area of any size circle that exists

ollivis