An open-topped cylindrical glass jar is to have a given capacity. Find the ratio of height to diameter if the area of glass is a minimum.

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- Apr 13th 2010, 12:21 PMrobertosavinOptimization Cylinder
An open-topped cylindrical glass jar is to have a given capacity. Find the ratio of height to diameter if the area of glass is a minimum.

- Apr 13th 2010, 01:11 PMArchie Meade
You need surface area in terms of a single variable, in order to easily differentiate,

so we can write h "in terms of" r.

The jar volume is

It's surface area is

To find the minimum surface area, differentiate surface area with respect to r

and set it to zero.

If this is zero then

corresponds to the jar being unrealistically stretched

into an "invisible" line.