Question

S(r)=2πrh+2πr^2. Find the instantaneous rate of change when r = 4 and height = 4

Answer 1

The surface area of a right circular cylinder of height 4 feet and radius r feet is given by \[S(r)=2πrh+2πr^2\]. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 4.

Answer 2

I have tried calculating the instantaneous rate of change but I got 32π. That isn't on of the answers.

Answer 3

I figured out the problem. For the people also confused with this question, it was very badly written. First, the formula which I was taught is \[\lim_{h \rightarrow 0} \frac{f(x+h) - f(x) }{ h }\] This problem also has it's own h. My reasoning is that both of these h's are the same. Wrong. What you have to do is convert tour limit variable to a different variable so the problem will make sense. At first I got 32π but after I got the right answer. I won't say it but just know that both h's are different.