document.write( "Question 174119: 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.The more simplified the better.
\n" ); document.write( "Many thanks \n" ); document.write( "

Algebra.Com's Answer #129007 by ptaylor(2198) $\"\"$ $\"About$

You can put this solution on YOUR website!
Area of Pool=A(pool)=pi(r^2)
\n" ); document.write( "Total Area=A(total)=pi(r+2)^2=pi(r)^2+4pi(r)+4pi
\n" ); document.write( "(expanding(r+2)^2=r^2+4r+4 and multiplying each term by pi)
\n" ); document.write( "Area of path=A(path)=A(total)-A(pool)=pi(r+2)^2-pi(r)^2=
\n" ); document.write( "A(path)=pi(r)^2+4pi(r)+4pi-pi(r)^2=
\n" ); document.write( "A(path)=4pi(r)+4pi=4pi(r+1) if r=2.5 m, then:
\n" ); document.write( "A(path)=4pi*(2.5+1)=4pi*3.5=14pi sq meters;
\n" ); document.write( "A(path)=14*3.14=43.95 sq meters
\n" ); document.write( "CK
\n" ); document.write( "A(total)=pi*(4.5)^2=63.585 sq meters
\n" ); document.write( "Area of Pool=pi*(2.5)^2=19.625 sq meters
\n" ); document.write( "63.585-19.625=43.96
\n" ); document.write( "43.96=43.96\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor \n" ); document.write( "

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