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Sagot :
If the surface area of the cylinder is 8cm , then the largest possible volume of such cylinder is (16/3)√(2/3π) cubic units .
In the question ,
it is given that ,
the cylinder is an open top ,
given that surface area = 8cm² ,
So , the surface area is = 2πrh + πr²,
8 = 2πrh + πr²
So , h = (8 - πr²)/2πr ,
the volume of the cylinder is (V) = πr²h ,
Substituting the value of h ,
we get ,
V = (8r - πr³)/2,
to find the largest volume , we differentiate it with respect to "r" and equate to 0 ,
we get ,
(8r - πr³)/2 = 0
On Simplifying we get ,
r = √(8/3π) ,
the volume is maximum when r = √(8/3π) ,
So , Volume is = ( 8(√8/3π) - π√(8/3π)³)/2
V = 4(√(8/3π)) - (4/3)(√(8/3π))
V = (8/3)√(8/3π)
V = (16/3)√(2/3π) cubic units .
Therefore , the maximum volume is (16/3)√(2/3π) cubic units .
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