Math Is Fun Forum

Kevin54756549

Guest

Help!

Extra fuel tanks carried in the cabin of a plane called ferry tanks.These tanks allow a plane to fly greater distances. A cylindrical ferry tank needs to hold 600 L of aircraft fuel.

a) What are the dimensions of two possible cylindrical fuel tanks?

b) What should the dimensions of the tank be to minimize the amount of aluminum used in its construction?

c) How do these dimensions compare to the optimal square-based prism fuel tank?

Please help me!! I don't even know where to start!!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help!

Hi Kevin54756549'

a)

The formula for the volume of this cylinder is:

Choose an h and solve for r and then choose an r and solve for h will give you two tanks.

b) You have not provided the thickness of the aluminum that comprises the tank. So the only thing I can minimize is the total surface area of the tank. For this you have to do some calculus. You want to minimize

subject to the constraint

Solve for h in B.

Substitute that into A. We get:

Differentiating that with respect to r will determine the extrema.

Setting that equal to 0.

This is a cubic that is easy to solve you get:

in decimal form. It is easy to determine that this is a minimum. Now plug into B to get h.

So the least amount of aluminum used in terms of TSA ( total surface area ) is done when

r = 45.70781497340833 cm
h=91.41562994681665 cm

TSA = 39380.57422012397 cm^2 of aluminum needed.

c) Try to do this one by yourself using what I have done in b. If you need help with it then just post back.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.