SOLUTION: A circular rug has an interior circle and two rings around the circle. a. Write a polynomial that represents the total area of the rug if the radius of the interior rug is r and

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A circular rug has an interior circle and two rings around the circle. a. Write a polynomial that represents the total area of the rug if the radius of the interior rug is r and       Log On


   

Question 1014254: A circular rug has an interior circle and two rings around the circle.
a. Write a polynomial that represents the total area of the rug if the radius of the interior rug is r and each ring is 1 ft. from edge to edge.
I got the answer to part a: Area= pi(4+4Runner+r^2)
Could you please help me with part b?
b. The interior circle of the rug has a diameter of 3 feet. What is the area of the rug? Leave your answer in terms of pi. Explain how you found your answer.
Thank you!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The answer to part a: can be written as Area=+pi%284%2B4r%2Br%5E2%29+ ,
or even as Area=+pi%2Ar%5E2%2B4pi%2Ar%2B4pi ,
but given r, it may be easier to calculate area using the equivalent expression
Area=+pi%28r%2B2%29%5E2 .

The radius of the interior circle is
r=diameter%2F2=3ft%2F2=1.5ft ,
so, using the "formula" for area found above, the area of the rug in square feet, is
Area=+pi%281.5%2B2%29%5E2=+pi%2A3.5%5E2=12.25pi .