6 we went over a similar problem in class suppose we want a right circ

Question

6. (We went over a similar problem in class) Suppose we want a right circular cylinder with an open top to have a volume of 64 ft. Find the dimensions (radius of the base and the height) of the cylinder that minimize the surface area,Follow the steps below.
Assume the radius of the base is x, and the height of the cylinder is h. Write h in terms of x. You will need the formula: volume of cylinder = area of base' height. Write the surface area of the cylinder as a function of x.The surface area of the cylinder = area of the base + area of the sides. Find the domain of the surface area function. Find the critical number(s) of the area function. Find the x value that yields the minimum surface area.Make sure to check that this x value indeed yields the minimum surface area. Find the minimum value of the area function over its domain. ) Check that h/x = 1. If h/x is not equal to 1, something went wrong.