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

### 1 Answer | Add Yours

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.**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes