
It seems pretty odd to change one of the variable when trying to do some optimization.

It seems pretty odd to change one of the variable when trying to do some optimization.
You want your volume to be $33$, hence you should not let it be an inequality. when we see $V$, we should directly replace it with $33$.
You do not want to minimize the gradient of the objective function, you want to minimize the objective function.
That is you want to minimize
$$\min _r\frac{66}r+2\pi r^2$$
$$s.t. r > 0$$