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

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SUMMARY

The discussion focuses on estimating the amount of tin in a closed tin can using differentials. The can has a diameter of 8 cm and a height of 12 cm, with a tin thickness of 0.04 cm. The correct differential formula for volume is established as dV = 2 * π * h * r * dr, where the values are substituted to calculate the estimated volume of tin. The final calculation confirms that dV = 2 * π * 12 * 4 * 0.04 accurately estimates the tin's volume.

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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!
 
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You are correct =).

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

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