Use sphere coordinates. Find the volume of the part of the ball ? < 9 that lies

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Explanation / Answer

Cartesian ---> Spherical: x² + y² + z² = ?² x = ?sinfcos? y = ?sinfsin? z = ?cosf f = polar; ? = azimuthal (varies text to text - this may cause confusion): ???dxdydz = ????²sinf d?dfd?; 0 = ? = 3; p/4 = f = p/3; 0 = ? = 2p INNER: ??²*sinf d? ; 0 = ? = 3; ?³/3*sinf; 0 = ? = 3; 9sinf MIDDLE: 9?sinf df; p/4 = f = p/3 -9cosf; p/4 = f = p/3 -9[cos(p/3) - cos(p/4)] -9[1/2 - v(2)/2] 9/2*[v(2)-1] OUTER: 9/2*[v(2)-1]?d?; 0 = ? = 2p 9/2*[v(2)-1]?; 0 = ? = 2p 9/2*[v(2)-1](2p - 0) ---------------- 9p*[v(2)-1

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