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Calculus Level 4

There are two circles:

  • \(\text{Circle-A}\) with equation \((x-10)^{2}+(y-10)^{2}=4\)
  • \(\text{Circle-B}\) with the equation \((x+10)^{2}+(y-10)^{2}=4\).

\(\text{Circle-A}\) revolves with \(y=-x\) as the axis while \(\text{Circle-B}\) revolves with \(y=x\) as the axis.

What is the total volume of the solid structure formed by the revolution of two circles?

Clarification and Caveat: The Structure will have more than one Steinmetz solid, so be carefull while entering your answer. And correct your answer to three decimal places. Assume the ring shaped structure formed by each circle to be a perfect cylinder.

This problem is original.


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