document.write( "Question 211692: A cylindrical can has a surface area of 60in(squared). Express the volume of the can as a function of the radius r. \n" ); document.write( "

Algebra.Com's Answer #159954 by HyperBrain(694) $\"\"$ $\"About$

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\n" ); document.write( "---
\n" ); document.write( "First hand, you should know the formula for the surface area of a cylinder which is SA=2*pi*r² + 2*pi*r*h
\n" ); document.write( "---
\n" ); document.write( "We are given the value SA=60. So...
\n" ); document.write( " $\"60=2%2Api%2Ar%5E2+%2B+2%2Api%2Ar%2Ah\"$
\n" ); document.write( "Factoring $\"2%2Api\"$ out,
\n" ); document.write( " $\"60=2%2Api%2A%28r%5E2+%2B+r%2Ah%29\"$
\n" ); document.write( "Dividing both sides by $\"2%2Api\"$ ,
\n" ); document.write( " $\"60%2F%282%2Api%29=r%5E2+%2B+r%2Ah\"$
\n" ); document.write( " $\"30%2Fpi=r%5E2+%2B+r%2Ah\"$
\n" ); document.write( "--
\n" ); document.write( "We now subtract $\"r%5E2\"$ to both sides of the equation.
\n" ); document.write( " $\"30%2Fpi-r%5E2+=+r%2Ah\"$
\n" ); document.write( "Then, we divide both sides by r.
\n" ); document.write( " $\"h=%2830%2Fpi-r%5E2%29%2Fr\"$
\n" ); document.write( "---
\n" ); document.write( "Then, we use the formula for volume $\"V=pi%2Ar%5E2%2Ah\"$
\n" ); document.write( "So
\n" ); document.write( " $\"V=pi%2Ar%5E2%2A%28%2830%2Fpi-r%5E2%29%2Fr%29\"$
\n" ); document.write( "Then
\n" ); document.write( " $\"V=pi%2Ar%2A%2830%2Fpi-r%5E2%29\"$
\n" ); document.write( "Then
\n" ); document.write( " $\"V=r%2A%2830-pi%2Ar%5E2%29\"$
\n" ); document.write( "And so,
\n" ); document.write( " $\"V=30r-pi%2Ar%5E3\"$
\n" ); document.write( "That's it. \n" ); document.write( "

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