In Exercises 37 and 38, you will need to know that a closed cylinder of radius R and length L has volume V = πR²L and surface area S = 2πRL + 2πR². The volume of a hemisphere of radius R is V = 2/3πR³ and its surface area is S = 2πR².

A bacterium is shaped like a cylindrical rod with two hemispherical “caps” on the ends. If the volume of the bacterium is fixed, what must be true about its radius R and length L to achieve minimum surface area?

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Radius R L L