



There is
a circular pond in front of the school. 


The pond
is 20 feet in diameter. 


The
school board wants to build a sidewalk around the pond. 


They want
to make the sidewalk 3 feet wide. 


What is
the area of the sidewalk? 





OK, so
the pond has a diameter of 20 feet. 


A
diameter is the distance 


from one
side of a circle to the other. 





A radius
is the distance 


from the
center of the circle to the edge. 


The
radius is one half of the diameter.. 





So the
radius of the pond is 10. 











The area
of the circle is equal to pi (3.14159 ...) 


times the
radius squared. 





Area = pr^{2} 





The area
of the pond is ... 





Area =
(3.1416)(10^{2}) 


Area = 314.2
square feet 





The
sidewalk is to be 3 feet wide. 


The
distance from the center of the circle 


to the
outside of the sidewalk is 10 + 3 = 13 feet. 





If we
didn't have a pond at all, 


but just
a round slab of concrete with a radius of 13 


the area
would be ... 





Area = p(13)^{2} 


Area = p(169)



Area = 530.9
square feet






But we DO
have a pond in the middle. 


The area
of the pond is 314.2 square feet. 











So the
area of the 3 foot wide walk, 


is the
area of the 13 foot radius concrete disk 


minus the
area of the 10 foot radius pond 


in the
middle of it. 





Area of walk =
530.9 sq. ft.  314.2 sq. ft. 


Area of walk =
216.7 sq ft. 





So this
is the strategy you use with the 


"border
around the edge" problems. 





Find the
area of the surface to the edge of the border 


Subtract
the area of the thing in the middle. 





copyright 2005 Bruce Kirkpatrick 
