Let the radius of the circle be r units.

We know that,
Area of the circle of radius r = πr ²

Since, The radius of the circle when it is doubled = 2r
⇒ Area of the circle when the radius is doubled = π(2r) ²
= 4πr ²

⇒ The ratio of the areas of the new circle to the given circle

= 4πr ² : πr ²

= 4 : 1

Hence,

The area increases by 4 times as the radius of circle is doubled.