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What happens to the area if you double the diameter of a circle?

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kenziekid | Student, College Freshman | eNoter

Posted April 4, 2013 at 6:54 PM via web

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What happens to the area if you double the diameter of a circle?

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted April 4, 2013 at 9:05 PM (Answer #1)

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Let the circle has the diameter of `d` and radius `r` (since radius is half of diameter it follows `r=d/2` ).

If we double our diameter `2d` radius is also doubled `(2d)/2=d=2r`. Now area of first circle is ` `

`A_1=r^2 pi`

and area of second circle is` `

`A_2=(2r)^2 pi=4r^2 pi=4A_1` 

As you can see the area of the second circle is four times greater than the area of the first circle.

So if we double the diameter of circle, its area will be quadrupled.

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