Find the volume of a Scallop Shell (Multiple Integrals)

jeudi 3 avril 2014

1. The problem statement, all variables and given/known data



Find the volume of the (half) shell, ignoring flanges, using the equation (in attachment).

Equations and variables given on the attachment.



2. Relevant equations







3. The attempt at a solution



a) I just need help by setting up the integral to find the volume.

What I did was taking the double integral with the region given by theta and r. This is my double integral:



∫(range of θ)∫(range of r) [z] drdθ



Is this integral correct?



b) Surface area = ∫∫[sqrt(z(r) + z(θ) +1]drdθ



where z(r) = partial derivative of r

and z(θ) = partial derivative of θ



Am I on the right track?








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