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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!

Show Open Topic

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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