The surface area of a right circular cylinder of height 5 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 6.

Question

zepdrix · Answer

$$\Large\rm S(r)=2\pi r h+2\pi r^2$$Hey Camila! :)
Have you learned your derivative shortcuts at this point?
Or do we have to use the limit definition for the derivative to find our instantaneous rate of change? -_-

anonymous · Answer

I know how to derive.

zepdrix · Answer

We're holding the height, h, constant at 5.$$\Large\rm S(r)=2\pi r \cdot 5+2\pi r^2$$Simplifies our function a little bit, which is nice.$$\Large\rm S(r)=10\pi r+2\pi r^2$$

zepdrix · Answer

So apply your power rule to each term, should be pretty straight forward :)
Are you getting confused because of all that pi nonsense mixed in?

anonymous · Answer

Yeah that was the part that confused me.

zepdrix · Answer

$$\Large\rm (10\pi x)'=10\pi(x)'=10\pi (1)$$Normal power rule, ignoring the constant coefficients :)

anonymous · Answer

So I would get 10π+4πr and plug in 6 for r?

zepdrix · Answer

$$\Large\rm S'(r)=10 \pi+4\pi r$$Good good good.

anonymous · Answer

So when I plug that in it would be 34π right?

zepdrix · Answer

Yayyy good job! *\c:/* Camila <*c:/*

anonymous · Answer

Haha okay thank you so much!

zepdrix · Answer

np