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In general, the volume
has total derivative
If the cylinder's height is kept constant, then
and we have
which is to say,
and 
are directly proportional by a factor equivalent to the lateral surface area of the cylinder (
).
Meanwhile, if the cylinder's radius is kept fixed, then
since
. In other words, and 
are directly proportional by a factor of the surface area of the cylinder's circular face (
).
Finally, the general case (
and 
not constant), you can see from the total derivative that is affected by both and in combination.
has total derivative
If the cylinder's height is kept constant, then
which is to say,
Meanwhile, if the cylinder's radius is kept fixed, then
since
Finally, the general case (