document.write( "Question 1137934: A block of metal is cast into a solid cylinder whose volume is 10cm^3. Show that the cylinder has a minimum surface area when r= 3 root (5 over pi). The ends are included. \n" ); document.write( "

Algebra.Com's Answer #755821 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( " $\"V+=+%28pi%29%28r%5E2%29%28h%29+=+10\"$ (1)

\n" ); document.write( " $\"S+=+2%28pi%29%28r%5E2%29%2B2%28pi%29%28r%29%28h%29\"$ (2)

\n" ); document.write( "Solve equation (1) for h in terms of r and substitute into equation (2), giving you an expression in terms of r only for the surface area.

\n" ); document.write( " $\"h+=+10%2F%28%28pi%29%28r%5E2%29%29\"$
\n" ); document.write( "

\n" ); document.write( " $\"dS%2Fdr+=+4%28pi%29%28r%29-20%2Fr%5E2\"$

\n" ); document.write( "Set the derivative equal to 0 and solve.

\n" ); document.write( " $\"4%28pi%29%28r%29-20%2Fr%5E2+=+0\"$
\n" ); document.write( " $\"4%28pi%29%28r%29+=+20%2Fr%5E2\"$
\n" ); document.write( " $\"r%5E3+=+20%2F%284%28pi%29%29+=+5%2F%28pi%29\"$
\n" ); document.write( " $\"r+=+%285%2F%28pi%29%29%5E%281%2F3%29\"$ \n" ); document.write( "

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