Solving using implicit differentiation 50. Physical science: waste storage. The

Question

Solving using implicit differentiation 50. Physical science: waste storage. The Waste Isolation Pilot Plant (WIPP) in New Mexico consists of large rooms carved into a salt deposit and is used for long- term storage of radioactive waste. (Source: www.wipp energy.gov.) A new storage room in the shape of a cube with an edge length of 200 ft is to be carved into the salt. Use a differential to estimate the potential difference in the volume of this room if the edge measurements have a tolerance of +2 ft. 12.6]

Explanation / Answer

Volume = edge length3

Let edge length = s

V = s3

Differentiating

dV = 3s2 dS

dV = 3(200)2(2) = 240000 ft3

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