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Question

The sum of the longest and shortest distances from the point (1,2,1) to the surface of the sphere x2+y2+z2=24 is

A
36
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B
46
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C
6
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D
2
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Solution

The correct option is B 46
Centre of the sphere is C(0,0,0) and radius is r=24=26
Let given point be P(1,2,1)
CP=(10)2+(20)2+(10)2=6
Hence, longest distance of P from the sphere is r+CP=36
and shortest distance of P from the sphere is rCP=6
Therefore, sum of the longest and shortest distances is 46.

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