document.write( "Question 1197132: a cylindrical vessel without a lid is to be made of metallic lamina of surface area 462 cm square. find the length of its base radius when its capacity is maximum \n" ); document.write( "

Algebra.Com's Answer #830323 by math_helper(2461) $\"\"$ $\"About$

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document.write( "Total area of open cyclinder is:
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document.write( "A(r) =    where r is radius and L is length of side\r
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document.write( "The volume is:
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document.write( "V(r) = \r
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document.write( "We can relate L to r by the given information:
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document.write( "   ===>  \r
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document.write( "So 
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document.write( "which reduces to:
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document.write( "Now the derivative of V with respect to r is:
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document.write( "Setting dV/dr to 0 and solving for r,   cm \r
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document.write( "Check by plugging in some values near 7.0cm for r, and compute corresponding volume:
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document.write( "r = 6.8  ==>  L = 7.4  ==>  V = 1074.9cm^3
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document.write( "r = 7.0  ==>  L = 7.0  ==>  V = 1077.6cm^3   <<< max capacity
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document.write( "r = 7.2  ==>  L = 6.6  ==>  V = 1076.5cm^3\r
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