Using Surface Integrals, calculate the area that vanishes with this rising tide

[daphnelee-mh]

Homework Statement

attached below

Relevant Equations

A=sqrt[1+(dz/dx)^2+(dz/dy)^2]dA

Please help to see whether it's correct to do in this way

 

[andrewkirk]

Yes that looks correct to me. I would put the limits of the inner integral the other way around - highest on the top - because the integral you gave will give you a negative number. But the size will be correct, and that's what really matters.

 

[daphnelee-mh]

Yes that looks correct to me. I would put the limits of the inner integral the other way around - highest on the top - because the integral you gave will give you a negative number. But the size will be correct, and that's what really matters.

Ya, I changed the inner integral and tried to evaluate, seems hard to get a finite answer

 

[haruspex]

The slope of the coast is quite small, so it will be very close to $\Delta(\pi r^2)$

 

[Adesh]

Ya, I changed the inner integral and tried to evaluate, seems hard to get a finite answer
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