Can we use the disk method in this integral?

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SUMMARY

The discussion centers around the application of the disk method in calculating the volume of a solid formed by the intersection of a sphere and a paraboloid. The user questions whether the disk method is appropriate given that the sphere penetrates the paraboloid beyond the intersection point at x=-1, extending to x=-sqrt(2). A participant clarifies that the formula 2πρ dρ represents a ring, not a disk, affirming that the user's calculations are correct.

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Amaelle
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Homework Statement
look at the image
Relevant Equations
cylindrical coordinates
Goodd day, I have a question regarding an exercice I have already posted
1613466709445.png

Bvu was very nice and provided this darwing
1613466770802.png

I already have the solution
1613466832087.png
But y question is :
can we use the disk method? because as you can see even though the intersection was at x=-1 the sphere goes deep into the paraboloid until x=-sqrt(2)?
so maybe the only way is to caluculate is to
1613468607815.png

Many thanks in advance!
 
Physics news on Phys.org
2\pi\rho d\rho is not disk but ring. So I think your calculation is OK.
 

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