The area of a circle with a radius r is given by pi*r^2 and the circumference of a circle with radius r is 2*pi*r.
Here we have a circle with a circumference 12*pi
2*pi*r = 12*pi
=> r = 6
Area = pi*6^2
The required area of the circle is 36*pi
Given the circumference of the circle is 12pi.
We need to find the area of the circle.
We know that the area of a circle is given by:
A = r^2 * pi such that r is the radius.
Also, we know that the circumference is given by:
C = 2*r * pi
But C = 12*pi
==> 2*r*pi = 12*pi
We will divide by 2pi.
==> r = 12pi/2pi = 6.
Then the radius is r= 6, we will substitute into A.
==> A = r^2 * pi = 6^2 * pi = 36pi.
Then the area of the circle in terms of pi is : A = 36pi square units.