The points in a rectangular waterproofed room with dimensions 20 x 20 x 20 are given coordinates by choosing one floor corner to be the origin so that the room lies in the first octant of space. A spherical balloon with center at (5, 4, 7) in the room is slowly filled with water until the balloon touches either the floor, ceiling, or one of the walls, whereupon the balloon then bursts. How deep is the water in the room? Explain. [From Example-39-in the notes, the volume of a sphere of radius Ris 1T R3 (3 1

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