Answer :

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.

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