SOLUTION: Find the waste in making the largest possible cylindrical rod from a bar of iron 2m long which has a cross section whose diagonal is 6cm.

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Question 1021148: Find the waste in making the largest possible cylindrical rod from a bar of iron 2m long which has a cross section whose diagonal is 6cm.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
I will assume that the iron bar has a square cross-section.
The diagonal of the square being 6cm ==> each side of the square is 6%2Fsqrt%282%29 cm.
==> the largest possible cylindrical rod would have a radius of 3%2Fsqrt%282%29 cm.
==> Volume of cylindrical rod is V+=+Bh+=+pi%2A%28%283%2Fsqrt%282%29%29cm%29%5E2%2A%28200cm%29+=+900%2Api+%28cm%29%5E3
But the volume of the iron bar is V+=+LWH+=+%28200cm%29%28%286%2Fsqrt%282%29%29cm%29%5E2+=+3600+%28cm%29%5E3
Therefore the amount of waste is
3600+%28cm%29%5E3+-+900%2Api+%28cm%29%5E3+=+772.57+%28cm%29%5E3, to two decimal places.