What is the value of the ratio of the surface area to the volume of the cylinder?

2/3

Step-by-step explanation:

Surface area is ...

... S = 2πr² + 2πrh = 2πr(r+h)

Volume is ...

... V = πr²h

Then the ratio of surface area to volume is ...

... S/V = (2πr(r+h))/(πr²h) = 2(r+h)/(rh)

For r= 4 and h=12, this ratio is

... S/V = 2(4 +12)/(4·12) = 2/3

Comment on this ratio

Unlike many ratios, this ratio is not a pure number. It has units of 1/ft. That means the ratio would be different if the dimensions of the cylinder were expressed in different units. If the dimensions were in inches, for example, the ratio would be 1/18 per inch.