2. Consider two spheres of equations r² + y² + z² = 2x - 2y + 4z-2 and x² + y² + ² = 4x+2y+4. (a) For which points P on the first sphere and Q on the second sphere is the distance d(P.Q) maximum? (b) Find the volume of the solid that lies inside both of the above spheres. (Hint: First show that in a sphere of radius R the volume of a spherical cap (or spherical dome) of hight h is V = = ™h² (3R – h).)

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Q: 4. Find the surface area of the part of the sphere x² + y² + z² = 1 above the plane z = 1/√2.

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