Estimating Tin Amount in Closed Tin Can using Differentials | Homework Help

[bodensee9]

Homework Statement

Sorry, this may sound dumb, but How do I 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?

Homework Equations

The volume of the can is V = pi*r^2h. So dV= 2*pi*rh*dr

The Attempt at a Solution

Could someone point out what I am doing wrong? I thought that since volume is pi*r^2h, and so dv = 2*pi*rhdr. So, wouldn't I just plug in 2*pi*4*12*0.04 to arrive at an estimate of the amount of the tin? Thanks so much!

 

[AngeloG]

You are correct =).

V = pi * r^2 * h
dV = 2 * pi * h * r * dR
dV = 2 * pi * 12 * 4 * 0.04