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

In summary, to estimate the amount of tin in a closed tin can with diameter 8 cm and height 12 cm and tin thickness of 0.04 cm, you can use differentials and the formula dV = 2pi*rh*dr to calculate an estimated volume of 9.6 cm^3.
  • #1
bodensee9
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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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  • #2
You are correct =).

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

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

1. How do you estimate the amount of tin in a closed tin can?

The amount of tin in a closed tin can can be estimated using differentials. This involves measuring the volume and thickness of the tin can, and using these values to calculate the surface area and volume of the can. Then, by determining the density of tin, the amount of tin in the can can be estimated.

2. What is the purpose of using differentials to estimate the amount of tin in a closed tin can?

Differentials are used to approximate values in situations where exact calculations are difficult or impossible. In the case of estimating the amount of tin in a closed tin can, differentials allow for a more accurate estimation by taking into account the variations in thickness and volume of the can.

3. What are the key factors that affect the accuracy of estimating the amount of tin in a closed tin can using differentials?

The accuracy of estimating the amount of tin in a closed tin can using differentials depends on the precision of the measurements taken for the volume and thickness of the can, as well as the accuracy of the density of tin used in the calculations.

4. Can differentials be used to estimate the amount of tin in any type of closed tin can?

Yes, differentials can be used to estimate the amount of tin in any type of closed tin can, as long as the necessary measurements and calculations are made accurately. However, the accuracy of the estimation may vary depending on the shape and size of the can.

5. Are there any limitations to using differentials to estimate the amount of tin in a closed tin can?

One limitation of using differentials to estimate the amount of tin in a closed tin can is that it assumes the can is a perfect cylinder, which may not always be the case. Additionally, any errors in the measurements or calculations can affect the accuracy of the estimation.

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