<PRE><B>Question 538428</B>
A rectangular sheet of perimeter 40 cm and dimensions x cm by y cm is to be rolled into a cylinder.  What values of x and y given the largest cylinder volume?
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2(x + y) = 40
y = 20 - x
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x = 2*pi*r
r = x/2pi
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Vol = pi*r^2*y = pi*(x/2pi)^2*(20 - x)
Vol = x^2*(20-x)/4pi
{{{Vol = (20x^2 - x^3)/4pi}}}
dV/dx = (1/4pi)*(40x - 3x^2) = 0
3x^2 = 40x
x = 40/3
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Local max at x = 40/3, y = 20/3 cm
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PS  Max volume = 94.314 cc

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