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.

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.

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.