document.write( "Question 969172: 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 410 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
\n" ); document.write( "\n" ); document.write( "x = \n" ); document.write( "

Algebra.Com's Answer #592179 by Fombitz(32388) $\"\"$ $\"About$

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$\"V=pi%2Ar%5E2%2Ah=410\"$
\n" ); document.write( " $\"SA=2pi%2Ar%5E2%2B2pi%2Ar%2Ah\"$
\n" ); document.write( "From the volume,
\n" ); document.write( " $\"h=410%2F%28pi%2Ar%5E2%29\"$
\n" ); document.write( "Substitute into the surface area equation,
\n" ); document.write( " $\"SA=2pi%2Ar%5E2%2B2pi%2Ar%2A%28410%2F%28pi%2Ar%5E2%29%29\"$
\n" ); document.write( " $\"SA=2pi%2Ar%5E2%2B820%2Fr\"$
\n" ); document.write( "Now surface area is only a function of the radius.
\n" ); document.write( "Take the derivative and set it equal to zero to find a min.
\n" ); document.write( " $\"d%28SA%29%2Fdr=4pi%2Ar-820%2Fr%5E2=0\"$
\n" ); document.write( " $\"4pi%2Ar=820%2Fr%5E2\"$
\n" ); document.write( " $\"r%5E3=820%2F%284pi%29\"$
\n" ); document.write( " $\"r%5E3=205%2Fpi\"$
\n" ); document.write( " $\"r=%28205%2Fpi%29%5E%281%2F3%29\"$
\n" ); document.write( " $\"r=4.03\"$ $\"cm\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"h=410%2F%28pi%2A4.03%5E2%29\"$
\n" ); document.write( " $\"h=8.04\"$ $\"cm\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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