Write a function f in simplest form that represents the ratio of the surface area of the volume

Question

The height of the right cylinder is 2r, where r is the radius

Answer 1

The important equations are:

       A_S = 2πrh       [that is, Circumference*height]

        V = πr²h        [that is, (area of circle)*height]

 

"Ratio" is:    R = A_S / V

 

      R = 2πrh / (πr²h)

      R = 2/r

 

Now, for this cylinder, h = 2r, then r = h/2

       R = 2/(h/2)

       R = 2*(2/h)            [to divide by fraction, invert and multiply]

       R = 4/h

 

The ratio, written as a function f of h, is:

        f(h) = 4/h