## Kids Say the Funniest Things

An elementary school teacher shares the most amusing things her students have written.

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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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An elementary school teacher shares the most amusing things her students have written.

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Login or Register to rate and post comments## Use string to solve the cylindrical gas problem

by Pfleming91As an alternative to the center of mass solution (which some sticklers have rejected) I would offer this method to the trucker. It has the advantage of not requiring any numerical work or calculus. I'm going the assume that the tank has unit radius. The solution can always be scaled by your favorite units. As others have noted, the area between the diameter and a chord parallel to the diameter is A + sin(2A)/2 where A is the (acute) angle that the diameter makes with a radius from the center of the circle to an endpoint of the chord. (This is really a challenge without pictures!) The trucker would like to find A such that pi/4 = A + sin(2A)/2. An easy way for him to do that which avoids messy calculation is to observe that the above equation is equivalent to pi/2 = 2A + sin(2A) and if he can determine 2A then he can easily find A. To find 2A: He finds a circular piece of cardboard (e.g., from a pizza box) of the same diameter as his gas tank and a piece of string whose length is one quarter the circumference of the cardboard circle. Starting at one end of a diameter he carefully wraps the part of the string around the cardboard circle up to a point (call it P) on the circumference so that the remainder of the string will drop down perpendicular to the diameter and just meet it. The straight part which is perpendicular to the diameter will then have length sin(2A) and the part wrapped around the edge of the cardboard circle will have length 2A. The trucker now can use the string to find A from 2A, draw the desired chord parallel to the diameter and measure the distance from the chord to the diameter and subtract it from 1. I hope this is enough of a description for the reader to draw a picture of the solution.

## Show Review - 1376

by peterirlenborn## Fuel Tank Solution

by bhartman117If 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)

## 14 inches...

by jackparkerThe necessary calculation can be found from http://mathworld.wolfram.com/CircularSegment.html mid page it says: To find the value of h such that the circular segment has area equal to 1/4 that of the circle, plug A=pi*R^2/4 into equation (18) and divide both sides by R^2 to get (23) where x=h/R. This cannot be solved analytically, but the solution can be found numerically to be approximately h=0.596027 or r=0.403973 So to measure a quarter tank, mark your dipstick at 14 inches from the top or 6 inches from the bottom.

## GaaaaLeeee

by craigaddisI take offense to your views of Gomer Pyle! What American hates Gomer Pyle???

## Solving the Cylinder Problem

by tadsMy brother told me about the problem you guys were trying to figure out with the truck driver's gas tank. I'm a math teacher and I tried my best to figure it out. If the tank measured 20in across in diameter, the quarter tank mark, (and 3/4 tank mark), should be 4 inches above or below the middle of the stick used to measure the diameter. I solved it by taking a formula for the area of the quarter of a circle, and set it equal to the formula of a circle's segment: (pi*r^2)/4 = ((A - SinA)r^2)/2 Then I solved for A, which is the central angle for the segment, and then I used the central angle to find the length. I hope this is helpful.

## The answer: 4 inches!

by AnonymousYour e-mail reviews have 2 answers so far: 6 inches, and 4 inches. The math teacher is correct that (about) 4 inches in depth equals one-quarter tank. By the way, the solution uses Trigonometry, and not Calculus (as mentioned on the show). So much for MIT.

## teach your girl to drive stick

by eborshardI usually love your show, but as a former 16-year old girl (roughly 16 years later) I took offense at the recommendation to teach a teenage girl to drive an automatic first, and a stickshift later. Thanks to my Dad's patience and my parents only having stickshift cars, I begrudgingly learned how to drive a manual transmission while all my friends had instant success in automatic cars. I have to say it was the best decision my parents made; since then I have been able to drive anything, from a 1969 VW bug in college to a fiesty pick-up truck for an on-campus recycling crew that only went into 3 gears. Teach her a stick and a stick only now - any idiot can drive an automatic. If we assume our teenage girls are so distracted by their cell phones and getting used to the steering wheel they will sink to that expectation. Teach them to handle a stick, check and change their own oil, and change a flat. They will feel confident for the rest of their lives, and can always fall back on an automatic and AAA later.

## 1/4 full at 6 inches on stick

by MikeVVYou had a great opportunity to show off your calculus skills! I used a spreadsheet to estimate the dipstick level and then checked it with a google.com search for "horizontal tank volume" The spreadsheet took an hour and the google search took 5 minutes! The fuel dip stick level for 1/4 tank remaining if the tank depth is 20 inches is 6 inches. (See http://www.1728.com/cyltank.htm)

## Oops! A GOOF! The answer is SIX!!

by cmoverdahl@aol.comI looked over my scratch paper, and saw an error! (Translation for MIT grads: a GOOF). The answer is, in fact, (about) 6 inches. (4 inches is what you calculate, but then it needs to be subtracted from the radius of 10).

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