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Question

An open cylindrical can has to be made with 100 square units of tin. If its volume is maximum, then the ratio of its base radius and the height is

A
2:1
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B
1:1
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C
1:2
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D
2:1
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Solution

The correct option is B 1:1
Let r be the base radius and h be the height of the cylinder.
Then, 2πrh+πr2=100
h=50πrr2
Volume of cylinder, V=πr2h=πr2(50πrr2)=50rπr32
dVdr=503πr22

dVdr=0
r=103π
d2Vdr2=3πr<0 at r=103π
Hence, V is maximum when r=103π
h=50π103π1023π=103π
So, when V is maximum, r:h=1:1

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