If the radius of a circle is increased by a factor of x, then the area is increased by what factor?

Given parameters;

  The radius of a circle is increased by a factor of x;

   let the radius of the circle  = r;

     The increased radius = rx

Area of a circle is given as πr²;

   Initially, the area of the circle  = πr²

where r is the radius

New area after the increase = π x (rx)²  = πr²x²

To compare the factor with which the area increased;

          Factor =  = πr²x² / πr²  = x²

The area increased by a factor of x²