Saturday, November 06, 2010

Stump the Chumps

This week on Car Talk, trucker Richard has a busted fuel gauge in his 18-wheeler. He's got a trusty stick to help measure the level of fuel in his cylindrical tank, but needs a formula to tell him whether that level means he's got 3/4 of a tank, or is running on fumes. You'd think two MIT grads would be able to help, but, well, you'd be wrong.

OK my smart friends, the tank measures 18 inches in diameter. Obviously when you dip the ruler into the tank you know that at 9 inches it means it's half full. What mark on the ruler would tell you the tank was one quarter full?

I came up with 7.1 inches. I used only geometry and as usual I did it in my head and can't explain exactly how I got my answer except I compared the area of an 18 inch square with an 18 inch circle. So, my smart friends, help me out. Tell me if I'm right because the problem with having Aspergers is that even when you don't want it, it's always there.

Remember, no calculus, no trig, no sliderulers, just a simple calculator.


u.f. said...

I tried for a few minutes, but can't get it. I can calculate it if you let me change the size of the tank, but that's not what you need.

Babba Gi said...

I don't understand how it matters what diameter the tank is.

Click-n-Clack finally told the trucker to find a guy with the same truck and a fuel gauge that works. Then have the guy call him up when he is at a quarter tank and go stick your ruler in his tank.

D- said...

Ok... I don't know if this is even close or not:
I used the area of an 18" circle to get the "area" (or volume). A = pi r-squared. Multiplied that by .25 to get quarter of that (Rep 1/4 tank of fuel). Used that result to solve for the new radius. Solved using the new chord and right triangle came up with about 7.8". Subtracted that sum from 9" Radius of tank. left about 1.2" of fuel in tank. Not much but add to that the length of the tank (unspecified).
Machinery"s Handbook gives the multiple formulas for actually "sticking a tank". Very complex but dead accurate. A lot if info required to know about the tank.

Babba-Gi said...

You need calculus, I'm just a victim of linear thinking. Like putting a square peg in a round hole.

u.f. said...


I started down the same path, but that changes the size (diameter) of the tank.

Babba, the diameter matters, because you asked how many inches represented 1/4 of a tank. The length doesn't matter, but the diameter.

Babba, I agree that calculus is needed. But I think you could come up with an approximation without it. Maybe with a series of 1" rectangles to represent the bottom half of the tank. (a cross-section, that is).


Babba Gi said...

The answer from car talk 5.9.