Discussion
A compact is 60 per cent dense green and sinters to 96 per cent. What is the approximate linear shrinkage?
Answer: B
Correct answer: about 14 per cent
Shrinkage is three-dimensional, so the linear figure is the cube root of the volume ratio: \[ 1 - \left(\frac{0.60}{0.96}\right)^{1/3} = 1 - (0.625)^{1/3} = 1 - 0.855 = 0.145, \] about 14 per cent. The 36 per cent offered is the volumetric shrinkage, \( 1-0.625 \), which is what results from forgetting the cube root.
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