A cylindrical gas container is closed at the top and open at the bottom ; if the iron plate of the top is 5/4 times as thick as the plate forming the cylindrical sides. The ratio of the radius to the height of the cylinder using minimum material for the same capacity is –
Text Solution
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V = π r 2 h
If k be the thickness of the sides then that of the top will be (5/4)k.
∴ S = (2 π rh) k + ( π r 2 ) (5/4) k ('S' is volume of material used)
or S = 2 π rk . 
+ 
π r 2 k = k 
∴ 
= k 
, ∴ r 3 = 4V/5 π
= k 
= π 
= + ive
When r 3 = 4v/5 π or 5 π r 3 = 4 π r 2 h
∴ r/h = 4/5.
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