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minimum surface area (material for construction) for a cylinder of given volume
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1

1

 show that the height of a closed cylinder of given volume and minimum surface area
is equal to its diameter
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write expressions for volume and surface area in terms of r and h
given volume is a constant
use that expression to eliminate h (or r ) from the expression for S
now diff. S twice w.r.t r
equate the first derivative to zero and solve for r
check for minima using the second derivative

answer and  some steps are given below
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integration formulae

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