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If the equation of a circle is x2 + y2 = r2, prove that the circumference of a circle is C = 2πr.
Solution:
To illustrate the problem, let's draw the graph of a circle as follows
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| Photo by Math Principles in Everyday Life |
If the equation of a circle is
We can rewrite the above equation as a function of x as follows
Take the derivative of the above equation with respect to x as follows
To get the length of a curve or circumference of a circle, consider only a quadrant as follows
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| Photo by Math Principles in Everyday Life |
The length of a curve is given by the formula
Substitute the value of dy/dx to the above equation, we have
Therefore, the circumference of a circle is
