For a circle with radius r, the circumference of the circle is 2*pi*r and the area is pi*r^2.
The circle we have here has an area of 36*pi, this gives the area of the circle as 6.
The circumference is 2*pi*6 = 12*pi. The width of the border is 2 cm. This gives the area of the border as 12*pi*2 = 24*pi
The area of the border around the circle is 24*pi cm^2
Area of the circle = pr^2m where r is the radius of the circle.
The area of the border of the two concentric circles with radii r1 and r2 is pi(r2^2-r1^2), where r2 and r1 are the external and internal circles.
If the 2cm border is external, then the radii are r2 = 8cm and r1 = 6cm.
If the 2cm border is internal, then r2 = 6cm and r1 = 4cm.
The area of the border = p(8^2-6^2)= 87.96 sq units or pi(6^2-4^2) = 62.83 sq cm.