radius and height of a cylinder with given volume and cost per m^2

i've got a warehouse composed from a cylinder and a roof with the shape of 1/2 sphere and a total volume (i think , it wasn't specified ) V=5*10^5 m^3 , i have to find the height H and radius R of the reservoir given a minimum cost of production for the cylinder of 8000 (currency)/m^2 ,and for the spheric part the cost is double of the cylinder part .

Mathematically speaking it's impossible to find either R or H or both with just the volume given . i think i'm either missing one of the variables R or H and the exercise is impossible or i have to use the production cost somehow but i don't know how .

Opinions ? is it possible ? Impossible ? if possible how ?

Answer 1

[John D'Errico]

I won't do your homework for you, and I truly hope nobody else does it either, as that would be inappropriate.

But it seems if the Volume is fixed, then you can write one simple equation that would allow you to relate the variables R and H. So while you cannot determine the two variables, you can do what has been requested.

That is, it appears you have been given the information to compute the cost of building that container, again as a function of the two size parameters that define it.

So what can you do? For example, you MIGHT decide to plot the governing relationship between R and H. It might be thought of as some nonlinear curve that lives in the (R,H) plane. Does any point along that curve have an associated cost to construct the container? (I hope so!) Can you find that point along the curve that minimizes the cost? (I hope so!)

Now you need to do the rest of the thinking, as if I told you anything more, I'd have already done your homework for you.

[Opariuc Andrei]

thx :)