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#1045: Pi Over Two Dopes

Original Air Date: 11.06.2010

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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. Happily, Tom and Ray are more on the ball in recommending a snow-worthy vehicle for Gail, her husband, and their 8 kids, and in helping Louann figure out why her Accord smells like burnt toast. Also, why "oil replenishment" is like vacuuming your living room without a bag, and Tommy goes on the rampage against--Gomer Pyle? All this and lots more, this week on Car Talk.

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Dave pronounces his nephew's new atomic watch "stupid" for a particular reason. But Dave's nephew proves him wrong. What was Dave wrong about? Find out!

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    gas tank problem

    by kpederso

    In order to figure out the 1/4 and 3/4 full heights of the gas tank, it is useful to consider only the circular cross section of the tank and first plot an estimate of what the volume (or area in this simplified case) of the tank would look like with height of the liquid in the tank. Once you have this plot, you can see that it resembles an inverted cosine function. Using the rules of adjusting cosine functions to fit values at certain points, the resulting function is: -((Pi*r^2)/2)cos(h*Pi/2*r)+(Pi*r^2)/2. By setting this function equal to (Pi*r^2)/2, you can solve for h and check that you get r. Once you are satisfied that the equation is correct, you can set it equal to (Pi*r^2)/4 (or 1/4th the total volume) and again solve for h, which gives a solution of 9.2 inches.

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