Question

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Answer 1

WOW...there's nothing like procrastinating on an assignment...
I'd suggest finding the volume of the water in the cave when it reaches a depth of three feet, and comparing that to how much water flows into the cave in ten minutes. This is in polar coordinates, so when you do your triple integral, don't forget the Jacobian \(\rho^2 \sin \phi\). What do you have for your integral so far?

Answer 2

How would you find the volume of the cave?

Answer 3

As I said, you'd do a triple integral through the region of water. If you just find the bounds on the region (sketching helps!), doing the integral becomes a snap.

Answer 4

A triple integral of the "function" \(1\).