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March 1, 2015

Wrotten Apple !

An apple is in the shape of a ball of radius 31 mm.
A worm gets into the apple and digs a tunnel of total length 61 mm,
and then leaves the apple. (The tunnel need not be a straight line.)
Prove that one can cut the apple with a straight slice through the center so that one of the two halves is not rotten.

2 comments:

pradeep sanchana said...

Diameter of the apple is 62cm.. And Worm digs the tunnel of 61 cm ..
as tunnel length is small it should be on one part of the apple.. When u cut it into two ... in parallel to the tunnel u wil get the other half which is not rotten.

Anonymous said...

the question was weak... what if the diameter of the tunnel is, lets say, 10mm?