document.write( "Question 266652: Suppose the volume must be 50in^3, What are the values for r and h that will minimize the amount of sheet metal required to obtain this volume. I know volume is v= (pi)r^2h. I also know the surface area is sa= 2(pi)rh+2(pi)r^2.
\n" ); document.write( "I have been working on this all day. Any help would be greatly appreciated. Thanks \n" ); document.write( "
Algebra.Com's Answer #195901 by Alan3354(69443)\"\" \"About 
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Suppose the volume must be 50in^3, What are the values for r and h that will minimize the amount of sheet metal required to obtain this volume. I know volume is v= (pi)r^2h. I also know the surface area is sa= 2(pi)rh+2(pi)r^2.
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\n" ); document.write( "Eliminate either r or h, then minimize Area wrt the remaining variable.
\n" ); document.write( "V = pi*r^2h = 50
\n" ); document.write( "h = 50/(pi*r^2)
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\n" ); document.write( "A = 2pi*rh + 2pi*r^2 = 2pi(rh + r^2)
\n" ); document.write( "A = 2pi(r^2 + 50/pi*r)
\n" ); document.write( "A = 2pi*r^2 + 100/r
\n" ); document.write( "dA/dr = 4pir - 100/r^2 = 0
\n" ); document.write( "pi*r - 25/r^2 = 0
\n" ); document.write( "r^3 = 25/pi
\n" ); document.write( "r =~ 1.99647 inches
\n" ); document.write( "h =~ 3.99295 inches
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\n" ); document.write( "It's a tough problem.\r
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