Question

The surface area of a right circular cylinder of height 4 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 = 4.

24π
16π
64π
20π

Answer 1

@zepdrix I got some of the work done, but stuck on a step

Answer 2

S(r) = 2pi r h + 2pi r ^2
S(r) = 2pi r * 4 + 2pi r ^2
S(r) 8 pi r + 2pi r ^2
(8 pi x)’ = 8pi(x)’ = 8 pi(1)

this is what I have so far

Answer 3

They said `when r=4`,
it looks like you plugged in h=4 though,
hmm that's no bueno :o

Answer 4

8pi +4pi (4)^2?

Answer 5

Oh I didn't read the question properly lolol :)
The first line says height of 4. woops!

Answer 6

I think it is 16?
8pi +4pi (4) =
8pi +8 pi = 16

Answer 7

\[\large\rm S(r)=2\pi r h+2\pi r^2\]Plugging in 4 for h,\[\large\rm S(r)=8\pi r+2\pi r^2\]Hmm, did you forget to differentiate the second term maybe?
Power rule on the r^2,\[\large\rm S'(r)=8\pi+2\cdot2\pi r\]

Answer 8

Okay, so 20?

Answer 9

20 pi

Answer 10

oh wait no

Answer 11

would it be 16pi?

Answer 12

\[\large\rm S'(r)=8\pi+4\pi r\]So plug in r=4,\[\large\rm S'(4)=8\pi+4\pi (4)\]

Answer 13

Ya it's probably 16.. or 20.. or something else :D

Answer 14

haha well thank you!