No, I'm crap at calculus.

I'm still a bit confused by responses like this. Even if you do it the hard way, it only needs simple trigonometry, not calculus (in UK terms, it's a GCSE question not an A-level question).

Consider a circular cross-section of the tank. The fuel comes halfway from the bottom to the centre. So by looking at the triangle formed by the centre of the tank, the point on the fuel's surface directly below the centre, and the "shore" of the fuel where it touches the edge, you can work out the angle at the centre, i.e. the angle that one side of the fuel subtends at the centre. It's the arc-cosine of 6/12, or 60 degrees. So the whole surface of the fuel subtends twice that, or 120 degrees, at the centre of the tank.

So what area of the cross-section is taken up by fuel? Well, it's the area of the 120-degree pie-slice shape, minus the two triangles. In other words, it's 1/3 of pi*12*12, minus twice 6*(12 sin 60). If you divide that by the total area of the cross-section, pi*12*12, you get the fraction of the total volume occupied by fuel. Multiply that by the capacity and you get the volume of remaining fuel.

Now all this needs a calculator, of course. But if the trucker's smart, he'll do this only once and calibrate his dipstick in actual fuel units.

Peter

Just reading this thread is making my head hurt. I think I'd rather get someone to fix the fuel gauge and be done with it.

You all are forgetting that the yard stick takes up volume, thus raising the level of the gasoline and giving a false reading. The solution I gave is the only easy and accurate way. The jar thing I'm not really going for. What are the chances of finding a jar that is proportionately equal to the tank?

The proportions don't make any difference. The only thing that you're calculating is the area described by the arc of a circle and the segment connecting its ends as a fraction of the total area of the circle. The depth of the cylinder is irrelevant in determining this.

Of course, you have to contend with the non-cylindrincal dissimilarities of both the tank and the jar. But we're not looking for precise measurement. Your method wouldn't provide that, either, as it's difficult to make the level of a tank the same after each filling. It also doesn't provide for arbitrary determination, which is certainly useful, if not actually required in this problem.

Most gas tanks have the ends of the cylinders rounded out while most jars are rounded in. Combine that with the yard stick giving a false reading and you have an inaccurate solution.

If the tank is exactly 100 gallons then accuracy shouldn't be a problem using my method. Plus, this method will work with any shape tank, making it more applicable to the real world.

Yeah, and it'd be real convenient when you get to an amount you haven't measured before.

BTW, since you're being annoyingly pedantic, six inches of a yardstick that measures a quarter of an inch by an inch would displace about 0.0065 gallons, which is far less than the precision you'd be able to get out of a pump. In addition, you're not taking into account the fuel you'd burn driving to a gas station. Or maybe you meant that you should call a truck to tow you to a gas station.

In all honesty, the levelness of the tank is likely to cause as much error as non-cylindrical abnormalities.

And you expect him to drive to the store and buy a jar?!

What do you think he pees in?

What do you think he pees in?

A High-flow toilet, smuggled in from Canada, of course.

-jk

What do you think he pees in?

depends...

What do you think he pees in?

depends...

No, that would be her