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If the equation of a circle is x2 + y2 = r2, prove that the area of a circle is A = πr2.
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
To get the area of a circle, consider only a quadrant as follows
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| Photo by Math Principles in Everyday Life |
The area of a curve bounded by the function, x-axis, and y-axis is given by the formula
Therefore, the area of a circle is
