Quandaries and Queries


Who is asking: Student
Level: Secondary

OK so here is my problem:

Gasoline is stored in a tank which is a cylinder on its side. Height of fuel is "h" meters and the diameter is "d". The length is "l".

I need to find the amount of gas in the tank when the height is h and also to calculate the fraction of how full it is.

Also, the part I am really confused on is this one,
E(h/d) is the error of the function of h/d, when h/d is used to measure how full the tank is. For what value of h/d is the error maximal?



Hi Jennifer,

In a response to an earlier question Harley gave a procedure to find an expression for the volume of gas in the tank. He used the radius r of the tank rather than the diameter d, but you can replace d r by d/2 . If you construct this expression and then divide it by the volume of the tank you can rewrite the expression in terms of the variable h/d . (I only checked this for the situation when h is less than d/2 , that is the tank is less than half full.) Let x = h/d then the expression for the amount of gas in the tank is a function of x, say G(x).

The second part of the problem is to estimate this function by h/d , which is x, so the error function E is given by

E(x) = |G(x) - x|

The task is to find the value of x that maximizes this function.



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