You are wondering how inaccuracies in the radius or height of your can effect th

Question

You are wondering how inaccuracies in the radius or height of your can effect the volume of the can. Use differentials to answer the questions below.
An error of percent in the radius will cause an error of approximately ......... percent in the volume of the can.
An error of percent in the height will cause an error of approximately .......... percent in the volume of the can.
Note that although the sentences above contain the word "approximately", the answers are actually determined precisely by the procedure with which we compute them. For example for the dependence on the radius you consider constant, and you use the differentials

Explanation / Answer

In general the differentials are used to find out the effect of a small change of the variables in the total expression! Over here the same can be done! So here Volume of the cone is 1/3 * p *r*r*h dV/V * 100 =( 1*3 * p *2*r*h/ (1/3*p*r*r*h)) =2/r *100 is the percentage dependence on the Radius and dV/V= (1/3 )*p*r*r / 1/3*p*r*r*h))=1/h *100 is the percentage dependence on the height

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