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1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
The solution to this problem is known. I want to use this exercise as a model to understand how to proceed when calculating the surface area of a geometric figure.
Question:
1) Why do we differentiate with respect to z to get dS?
I'd say because in the constraining figure (in this case a cylinder which lies on the xy plane), while we move through the figure, we're changing ##z## coordinate.
I guess that if the cylinder were to lie on the, say, yz axis we'd differentiate with respect to x.
Am I right?
2. Relevant equations
3. The attempt at a solution
The solution to this problem is known. I want to use this exercise as a model to understand how to proceed when calculating the surface area of a geometric figure.
Question:
1) Why do we differentiate with respect to z to get dS?
I'd say because in the constraining figure (in this case a cylinder which lies on the xy plane), while we move through the figure, we're changing ##z## coordinate.
I guess that if the cylinder were to lie on the, say, yz axis we'd differentiate with respect to x.
Am I right?
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