Posted by **john** on Wednesday, May 16, 2012 at 11:58pm.

a rectagular sheet of metal has perimeter 36 meters. maximize the volume if the sheet is rolled into a cylinder

- calculus -
**Steve**, Thursday, May 17, 2012 at 5:43am
if the sheet is x by y,

2x+2y=36

x = 18-y

rolled parallel to x,

v = pi r^2 x

where r = y/2pi

v = pi (y/2pi)^2 (18-y)

= y/4pi (18-y)

dv/dy = (9-y)/2pi

dv/dy = 0 when y=9

as expected, it's a 9x9 square sheet.

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