# Project - M easuring gas by I ntegration By It has been...

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Measuring gas by Integration By:

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It has been brought our attention that your measuring stick, to measure the gas in the gas tanks has been stolen. You need us to try and find an equation that gives the number of gallons left in the tanks by using integration. You would also like us to find the number of gallons left in the tanks using Trigonometry and Geometry. After doing that, you would like us to mark a stick for every 5000 gallons in the tank. We know that the Tank has a100 inches in radius and is 400 inches in length. For question one, We used the following picture, We put the origin in the middle of the circle. From there, we drew a line across the bottom half of the circle as shown. Then, we drew a right triangle, with the hypotenuse being “r” and the height being “y”. We used the Pythagorean theorem an solved for the missing side and got - r2 y2 . So, with this we used the following equation for our integration: - - - 2L231 rd rr2 y2 . We multiplied the whole equation by two because - r2 y2 is only half of it, we then divided by 231 because the original units were in cubic inches and we needed gallons.
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