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Question -

Of all the closed cylindrical cans (right circular), of agiven volume of 100 cubic centimetres, find the dimensions of the can which hasthe minimum surface area?



Answer -

Let r and h bethe radius and height of the cylinder respectively.

Then, volume (V) of the cylinderis given by,

Surface area (S) of the cylinderis given by, 

 

By second derivative test, the surface area is theminimum when the radius of the cylinder is 

 

Hence, the requireddimensions of the can which has the minimum surface area is given by radius =

 and height = 

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