I have developed the formula to determine the radius of a cylinder with a fixed volume: f (

Agostarawz

Agostarawz

Answered question

2022-07-02

I have developed the formula to determine the radius of a cylinder with a fixed volume:
f ( x ) = V π 3  
Substituted into the formula for the surface area of a cylinder, I get the following function. This would give me the minimum surface area of a cylinder for a given volume.
S ( V ) = 2 π ( V π 3 ) 2 + 2 π ( 2 V π 3 )
However, my assignment for class asks for a rational function for this problem. How could I take my existing function and make it rational?

Answer & Explanation

Immanuel Glenn

Immanuel Glenn

Beginner2022-07-03Added 12 answers

I assume the cylinder in question has h = r, so that:
r = V / π 3
The surface area is then:
A = 2 π r 2 + 2 π r h = 4 π r 2 = 4 ( π V ) 2 / 3
This of course is not a rational function in V (and never will be), but is a rational function in r. Perhaps this is what the assignment means?

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