The radius of a circle of area a and circumference c is doubled. find the new area of the circle in terms of
a.

By definition, the circumference of a circle is:
 
 The area of a circle is:
 
 Where,
 r: radius of the circle.
 When the radius is double, then the new area is:
 
 Rewriting we have:
 
 In terms of a we have:
 
 
 The new area of the circle in terms of a is: