Question

How does doubling the diameter of a circle change its area?

Answer 1

If the diameter of a circle is doubled, its area increases `4` times.

Explanation:

Let the original diameter be `d`, then the radius is `r=d/2`, and the area is : `A=pi*(d/2)^2=(pi*d^2)/4`

If the diameter is doubled, then `d_1=2d`

The area `A_1` is:

`A_1=(pid_1^2)/4=(pi*(2d)^2)/4=(4pid^2)/4=pid^2`

So `A_1=4A`

The new area is `4` times larger.