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

Expert Answers
justaguide eNotes educator| Certified Educator

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

neela | Student

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.