i do this question correctly but i am confused about something in (c)

i don't understand why it shouldn't be

?z

why the surface area S is treated as a constant? S is a function of r and h, S changes as r or h changes. Although V is a function of r and S after expressing h in terms of r and S, then S is not a variable?

for example, the perimeter P of a rectangle is given by and its area , then and if i differentiate both sides then should it be or ?

any explanation will be appreciated! thanks.