This is very strange. You are doing Calculus yet you say "However, the pi is scaring me. Pi is a constant and so far I have only learnt doing it with variables." Have none of the problems you have done involve "2" or "3"? Those are also constants. Even if you had a problem with, say , "xyz", there is a "1" implied that is a constant.

You then have " " and " ". Where did those come from? You say you are using the "Lagrange multiplier method" but if so where is the multiplier? Yes, 2rh= 4r implies h= 2r but did you notice that immediately implies r= 0 or r= 2 (which isnota solution)? And your third "equation", is not even an equation!

The idea of the "lagrange Multiplier Method" is that any maximum or minimum of F(x,y,z) subject to the constraint G(x,y,z)= constant occurs where for some constant .

Here, F is , the volume function, and G is , the total surface area.

, where I have arbitrarily written for a unit vector in the "r direction" and for a unit vector in the "h direction".

.

is, then,

Setting the components equal we have the two equations

and .

Those, together with the equation , give three equations to solve for r, h, and .

Since it is not necessary to find to solve this problem, it is often simplest to eliminate bydividingone equation by another:

which reduces to

.

Solve that, together with .