SOLUTION: a circular pond has a radius of 10 feet. there are plans to build a paved path around the pond. if the path is to be 2 feet wide, how many square feet of paving are needed?

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: a circular pond has a radius of 10 feet. there are plans to build a paved path around the pond. if the path is to be 2 feet wide, how many square feet of paving are needed?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 864599: a circular pond has a radius of 10 feet. there are plans to build a paved path around the pond. if the path is to be 2 feet wide, how many square feet of paving are needed?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The area of just the pond only is exactly pi%2Ar%5E2+=+pi%2A10%5E2+=+100pi square feet.


The radius of pond + the path is 10+2 = 12 ft, so the area of the pond+path is is exactly pi%2Ar%5E2+=+pi%2A12%5E2+=+144pi square feet.


The area of just the path only is equal to the difference of the two areas:


Area of Path DISABLED_event_Only= (Area of Pond+Path) - (Area of Pond Only)


Area of Path DISABLED_event_Only= 144pi+-+100pi


Area of Path DISABLED_event_Only= %28144+-+100%29pi


Area of Path DISABLED_event_Only= 44pi


The exact area of the path only is 44pi square feet. If you use the decimal approximation of 3.14 for pi, then the approximate area of the path is 44pi=44%2A3.14=138.16 square feet.


Keep in mind that pi goes on infinitely in terms of the decimal expansion. So use more decimal digits of pi to get a more accurate picture of the approximate area.