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

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### 1 Answer

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.**