Question

The height of a right cylinder is 2r, where r is the radius. Write a function f in simplest form that represents the ratio of the surface area to the volume.

Answer 1

F = 3/r.

The formula for the volume of a cylinder is

V=πr²h.  We know that h=2r, so this gives us:

V = πr²(2r) = 2πr³

The surface area of a cylinder is the sum of the areas of all of the faces.  The bottom and top are circles, whose areas are both given by A=πr².  The lateral area of a cylinder is given by the circumference multiplied by the height.  C = 2πr, and the height is 2r, so the lateral area would be

A=(2πr)(2r)= 4πr².  This gives us a total surface area of

SA = 4πr²+πr²+πr² = 6πr².

The ratio of surface area to volume would be:

SA/V = 6πr²/2πr³.  After simplifying, we have f=3/r.