how to know the value of circle
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. Firstly we find the radius
then the solving the question
then the solving the question
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The Area of a Circle
So you have a circle. What is the area of that circle? Surely everyone remembers that the area of a circle is:
la_te_xi_t_14
Where Pi (π) is of course the number and r is the radius of the circle. Where does this formula come from? One method of obtaining this equation is to integrate dxdy over the area of a circle. Well, you probably wouldn’t want to do that in cartesian coordinates – but you get the idea.
I recently saw a graphical derivation of the area of a circle. Let’s say you start with a circle and break it into 4 wedges. The area of the 4 wedges should be the area of the circle (since that’s where they came from).
sketches_fall_14_key4
Maybe you can see where this is going – but what happens if I cut thinner wedges? Here is another way to break it up with even more wedges.
sketches_fall_14_key5
It’s really starting to look like a rectangle now. Eventually, it would be almost a perfect rectangle with enough wedges. The vertical side of this rectangle is the radius of the circle and the length of the side is half of the circumference (so, 2πR). Yes, the area of this rectangle would be πR2. That’s the area of a circle. Yes, this is sort of cheating. It’s cheating because it assumes the circumference is 2πR. But still, it’s something.
So you have a circle. What is the area of that circle? Surely everyone remembers that the area of a circle is:
la_te_xi_t_14
Where Pi (π) is of course the number and r is the radius of the circle. Where does this formula come from? One method of obtaining this equation is to integrate dxdy over the area of a circle. Well, you probably wouldn’t want to do that in cartesian coordinates – but you get the idea.
I recently saw a graphical derivation of the area of a circle. Let’s say you start with a circle and break it into 4 wedges. The area of the 4 wedges should be the area of the circle (since that’s where they came from).
sketches_fall_14_key4
Maybe you can see where this is going – but what happens if I cut thinner wedges? Here is another way to break it up with even more wedges.
sketches_fall_14_key5
It’s really starting to look like a rectangle now. Eventually, it would be almost a perfect rectangle with enough wedges. The vertical side of this rectangle is the radius of the circle and the length of the side is half of the circumference (so, 2πR). Yes, the area of this rectangle would be πR2. That’s the area of a circle. Yes, this is sort of cheating. It’s cheating because it assumes the circumference is 2πR. But still, it’s something.
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