Calculus problem help (attachment below)

Question

anonymous · Answer

attachment

tkhunny · Answer

Please show your work.

anonymous · Answer

$$V = \pi r^2h$$
$$r = 14$$
$$h = 65$$

anonymous · Answer

$$\frac{ dr }{ dt } = \frac{ 1 }{ 96 }$$

anonymous · Answer

I somehow got this:

anonymous · Answer

$$dV = \frac{ 12740 \pi }{ 96 }$$

anonymous · Answer

But I'm pretty sure that's wrong

tkhunny · Answer

Great.  Do something that you are pretty sure is right.

Why do we care about the volume?  We're only painting the sides.

anonymous · Answer

Well, the radius is changing, not sure if that accounts for anything

tkhunny · Answer

No Paint: $V_{0} = \pi r^{2}h$
Yes Paint: $V_{1} = \pi (r+1/8")^{2}h$

Your task, rather than calculate it directly, is to approximate the change in the volume, given dr = 1/8"

tkhunny · Answer

h = 65 ft

$V(r) = 68\pi r^{2}$

Are you seeing it, yet?

tkhunny · Answer

Forget about dr/dt.  There is no time structure in this problem.

anonymous · Answer

Where did 68 come from?

anonymous · Answer

And wouldn't you have to convert 1/8 inches to feet?

tkhunny · Answer

Typo. Make that 65. You should have told me that answer.

$V(r)=65πr^{2}$

anonymous · Answer

I don't see anything

tkhunny · Answer

I don't have to convert it, you do.

tkhunny · Answer

Calculate dV/dr

anonymous · Answer

130pir(dr)

tkhunny · Answer

$dV = 130\pi \;r\;dr$

Good.  Substitute the known values.

anonymous · Answer

I'm getting 455pi/24

tkhunny · Answer

What did you use for r and dr?

anonymous · Answer

r = 14, dr = 1/96. I just simplified, and I got it correct.

tkhunny · Answer

Perfect.