As concrete dries, it shrinks—the higher the water content, the greater the shrinkage. If a concrete beam has a water content of w kg/m3, then it will shrink by a factor
S =
0.032w − 2.5
10,000
where S is the fraction of the original beam length that disappears due to shrinkage.

(a) A beam 12.027 m long is cast in concrete that contains 550 kg/m3 water. What is the shrinkage factor S?

How long will the beam be when it has dried? (Round your answer to three decimal places.)

(b) A beam is 12.047 m long when wet. We want it to shrink to 12.033 m, so the shrinkage factor should be
S = 0.0012.
What water content will provide this amount of shrinkage? (Round your answer to the nearest whole number.)