HP42s first major program (Double Integral) Best way to approach?

[Albert Chan]

If we assume drilling though the pipe, penetrating both side, we do not need "2 /" correction.
In other words, I = bore-hole removed volume

XCas> [a,b,c] := [24,29,12] .* 2      // convert to diameter values
XCas> gaussquad(sqrt(c^2-x^2) * (sqrt(b^2-x^2) - sqrt(a^2-x^2)), x = 0 .. c) → 4651.24643662

// intersection of 2 cyclinders with radius 1 (diameter 2), volume = 16/3

XCas> b := c := 2
XCas> int(sqrt(c^2-x^2) * sqrt(b^2-x^2), x = 0 .. c) → 16/3