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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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This Week's Puzzler

Can the sales-kid explain where the dollar missing from the record store register went? Can you?

Last Week's Puzzler

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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Kids say the funniest things... and Tom and Ray have the examples to prove it!

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Fuel Tank Solution

by bhartman117

If you want to use calculus, here is the solution: Come up with a 2-D section of a circle: x^2 + y^2 = r^2, or x^2 + y^2 = 100. Set y = sqrt(100-x^2). Integrate from t to 10, t being the distance from the center of the fuel tank down to the surface of the fuel at 1/4 full. Set this integral equal to 1/8 the the Area of the full circle (it's one-eight since you're only calculating for positive values of the y-axis). 1/8 of the area is 39.27 in^2. t comes out to be about 4.04. Thus, the distance from the top of the fuel tank is 14.04 inches. (Note, integrating sqrt(100-x^2) is difficult and I had to use an online integrator calculator)

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