# Use differentials to estimate the amount of material in a closed cylindrical can that is 30 cm...

## Question:

Use differentials to estimate the amount of material in a closed cylindrical can that is 30 cm high and 12 cm in diameter if the metal in the top and bottom is 0.2 cm thick, and the metal in the sides is 0.05 cm thick.

## Approximation using differentials:

We can use differentiation to approximate small changes in a quantity. For a quantity {eq}F=g\times h {/eq}, the approximation of the quantity is {eq}dF {/eq} which is calculated by the use of partial derivatives

i.e. {eq}dF=\frac{\partial F}{\partial g}\cdot dg+ \frac{\partial F}{\partial h}\cdot dh {/eq}

Volume {eq}V=\pi r^2h {/eq}

The total differential of V is dV

{eq}dV=\frac{\partial V}{\partial r} \cdot dr+\frac{\partial V}{\partial h} \cdot...

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