What is the area of a border of width 2 cm around a circular shape of area 36*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.