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 for

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 for      Log On


   

Question 174098: 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 stanbon(75887) 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.
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Procedure: Draw the picture including the path around the circular pool.
Subtract the area of the pool from the area of the pool with its path.
That gives you the area of the path.
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Area of the pool alone = pi*r^2 = pi*2.5^2 = 6.25pi sq meters
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Radius of the pool/path combination = r+2 meters
Area of the pool/path combination = pi*(2.5+2)^2 = 20.25pi sq. meters.
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Formula:
Area of path = Area of pool/path - Area of pool
Area of path = [pi*(r+2)^2 - pi*r^2
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Your Answer:
Area of path = [20.25pi - 6.25pi] sq. meters
Area of path = 14pi sq meters
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Cheers,
Stan H.