What center should a sphere of radius 2 have so that it sits on the xy plane with its bottom (lowest point in the z direction) just touching the origin?
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What center should a sphere of radius 6 have so that it sits on top of the previous sphere (that is, higher in the z direction, touching the previous sphere at just one point)?
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What are the two opposite corners of a box that tightly contains the previous two spheres (and whose edges are parallel to the axes)?
First give the corner with all positive coordinates:
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Then give the corner opposite that one:
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What center should a sphere of radius 8 have so that it sits on top of the point ?
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What center should a sphere of radius 13 have so that it hangs just below the previous sphere, touching it at just one point?
Answer: (
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You can earn partial credit on this problem.