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The area of a circle of radius 1 is T units squared. Use scaling to explain why the area of a circle of radius r is T/p? units squared.

The area of a circle of radius 1 is T units squared. Use scaling to explain why the-example-1
User Anomepani
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Given a figure with an area A, if we use a scale factor of b on its dimensions, the new area A' will be:


A^(\prime)=b^2\cdot A

Now, if we have a unitary circle (radius = 1) of area A, the scale factor to go to a circle of radius r will be r, because 1*r = r. Then, using the equation above:


A^(\prime)=r^2\cdot A

Additionally, we know that the area of the unitary circle is:


A=\pi\text{ units squared}

Finally, we conclude:


A^(\prime)=\pi\cdot r^2\text{ units squared}

User Spurdow
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