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I just found this thread, which handily has the same exact problem. The OP says that dh is = 0 though, and I don't quite understand why he does that.

1. The problem statement, all variables and given/known data

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 12 cm if the tin is 0.04 cm thick. (Round the answer to two decimal places.)

3. The attempt at a solution

I wasn't really sure how to start this one, but I took a stab at it.

[itex]V=\pi*r^{2}*h[/itex] where r = D/2. I then found the differential of this.

[itex]dV=\frac{\pi}{4}D^{2}*dh + \frac{\pi}{2}hD*dD[/itex]

I put in 8 for D, 12 for h, and .04 for dH and dD. I got 8.04cm^{3}, but that is apparently wrong, according to the homework.

So I tried using the area instead.

[itex]A=hD\pi + \frac{\pi}{2}D^{2}*dD[/itex]

Differentiating, I get

[itex]dA=\pi*Ddh + \pi(h+D)*dD[/itex]

I put in 8 for D, 12 for h, and .04 for dH and dD. I got 3.52, but this answer is also incorrect.

Under normal circumstances I would calculate the area of the can and multiply by .04, but my gut feeling tells me this is wrong as well. Am I supposed to multiply dA by dV?

I only have one chance left to get it right, so I was hoping to figure it out here first. Thanks.

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# Homework Help: Using differentials for stuff?

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