In Exercises 37 and 38, you will need to know that a closed cylinder of radius R and length L has volume V R 2 L and surface area S 2RL 2R 2 The volume of a hemisphere of radius R is V 2 3R 3 and its surface area is S 2R 2 A bacterium is shaped like a cylindrical rod If the volume of the bacterium ...

Let S denote the surface area of the bacterium The ...

In Exercises 37 and 38, you will need to know that a closed cylinder of radius R

Question:

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. If the volume of the bacterium is fixed, what relationship between the radius R and length H of the bacterium will result in minimum surface area?