SOLUTION: Hello, I have a question that im extremely stuck on.The question is as follows:- A circular pool has a radius r. It is surrounded by a path which is 2 metres wide. Work out a formu

Algebra ->  Surface-area -> SOLUTION: Hello, I have a question that im extremely stuck on.The question is as follows:- A circular pool has a radius r. It is surrounded by a path which is 2 metres wide. Work out a formu      Log On


   

Question 174100: Hello, I have a question that im extremely stuck on.The question is as follows:- A circular pool has a radius r. It is surrounded by a path which is 2 metres wide. Work out a formula for the area of the path and give its area when r=2.5 metres.Please could you show the step by step guide on how i would work this out.Many thanks
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A circular pool has a radius r. It is surrounded by a path which is 2 metres wide. Work out a formula for the area of the path and give its area when r=2.5 metres.Please could you show the step by step guide on how i would work this out.Many thanks
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The area of the path is the area of the outside circle, minus the area of the inside circle (called an annulus).
The inside circle is the pool, radius r. The outide circle has a radius of r+2.
Area outside = pi%2A%28r%2B2%29%5E2
Area inside = pi%2Ar%5E2
AO - AI = pi%28r%2B2%29%5E2+-+pi%2Ar%5E2
= pi%2A%28%28r%5E2+%2B+4r+%2B+4%29+-r%5E2%29
= pi%2A%284r%2B4%29
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For r=2.5:
= pi*(10 + 4)
= 14*pi
=~ 43.98 sq meters