Please check your question. It should be a closed right circular cylinder.
Let r be the radius of the base and h be the height of the cylinder.
Let S be the total surface area.
Let Volume of the cylinder be V
Thus, we have,
Now differentiating the above function with respect to r, we have
For maximum, or minimum, we have
with respect to r, we obtain,
Hence, V is maximum when h = 2r, i.e. when the height of the cylinder is equal to the diameter of the base.