document.write( "Question 990244: You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 170 cm^3, what values of h and r will minimise the total surface area (including the top and bottom faces)? Give your answers correct to 2 decimal places as a list [in brackets] of the form: [ h, r ]
\n" ); document.write( "for constants h (height), r (radius), in that order.\r
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Algebra.Com's Answer #610382 by josgarithmetic(39629) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"v=pi%2Ah%2Ar%5E2\"$ , $\"s=2%2Api%2Ar%5E2%2B2pi%2Ar%2Ah\"$ , and $\"v=170\"$ .\r
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\n" ); document.write( "\n" ); document.write( "s is for surface area of the can.\r
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\n" ); document.write( "\n" ); document.write( "v formula gives $\"h=v%2F%28pi%2Ar%5E2%29\"$
\n" ); document.write( " $\"s=2pi%2Ar%5E2%2B2pi%2Ar%28v%2F%28pi%2Ar%5E2%29%29\"$
\n" ); document.write( " $\"s=2pi%2Ar%5E2%2B2v%2Api%2F%28pi%2Ar%29\"$
\n" ); document.write( " $\"highlight%28s=2pi%2Ar%5E2%2B2v%2Fr%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Find ds/dr and equate to 0, and solve this for r.\r
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\n" ); document.write( "\n" ); document.write( " $\"ds%2Fdr=4pi%2Ar%2B2v%28-1%29%28r%5E-2%29\"$
\n" ); document.write( " $\"ds%2Fdr=4pi-2v%2Fr%5E2=0\"$
\n" ); document.write( " $\"highlight_green%28%284pi%2Ar%5E2-2v%29%2Fr%5E2=0%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Actually, you are looking for $\"highlight%282pi%2Ar%5E2-v=0%29\"$ ------Solve this for r. \n" ); document.write( "

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