Sensitivity Analysis of a Cylinder's Volume
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A cylindrical steel storage tank is to be built that is 10ft tall and 4ft across in diameter. It is known that the steel will expand/contract with temperature changes; is the overall volume of the tank more sensitive to changes in the diameter or in the height of the tank?
partial-derivativestotal-differentialsensitivity-analysismultivariable-functionsvolume-of-cylinderrates-of-changelinear-approximationapplied-calculuscalculus-iiigeometry
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What you need first
- The formula for the volume of a cylinder
- How to compute partial derivatives
- The concept of the total differential
What this problem tests
Tests the ability to compute partial derivatives, construct a total differential, and interpret the coefficients as sensitivities.
This is a classic application of partial derivatives in a multivariable calculus course, demonstrating how the total differential can be used for sensitivity analysis or error propagation.
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