1. Describe your methods of measuring the dimensions of the library.For both the length and width, we measured the smaller squares outside of the library (approx. 60cm per square) and counted how many squares it took to go from one side of the building to the other which ended up being a total of 55 squares for both width and length. For the height, we took the height of the 3rd floor library using the meter stick inside the library which was 248 cm and multiplied it by 26 (floors). Those were our methods of measuring the dimensions of thelibrary. 2. Calculate the volume of the library using the dimensions you measured, and record them for the second part of this lab.Trial Length(m) Width(m) Height(m) Volume(m^3) Kyle 33.50 33.50 65.00 72946.25Orrin 33.55 33.55 69.20 77891.69Vicky 33.00 33.00 64.48 70218.72Sam 33.20 33.20 66.00 72747.8433.50m x 33.50m x 65m = 72946.25m^333.55m x 33.55m x 69.20m = 77891.69m^333m x 33m x 64.48m = 70218.72m^333.2m x 33.2m x 66m = 72747.84m^3Representing your data3. Calculate the mean and standard deviation of each of the three dimensions (length/width/height) using the four measurements taken by your table using the same method.Mean length:33.3125mStandard deviation of length:0.2247mMean width: 33.3125 mStandard deviation of width:0.2247mMean height: 66.17 m Standard deviation of height: 1.8327m4. Calculate the volume of the library using the means for each dimension. Just making a educated guess, what do you think is the uncertainty in this volume? What was the reasoning behind your guess?(33.3125 m) * (33.3125 m) * (66.17 m) = 73430.348m3 There is uncertainty in this volume due to the height. Our uncertainty estimate is about 10,000 m3. We estimate this uncertainty because it is hard to determine the height of the building since we don’t know if all the floors are of the same height. We also did not account for the fact that the basement and the 1st floor of the library are slightly bigger than floors 2-26.5. What is the average and standard deviation for the volumes you have calculated using this method?’Average: 72818.4499m3Standard Deviation: 1854.054m36. Calculate the percent error on each of the three dimensions. |(72818.4499m3 - 98353m3 )| / 98353m3 x 100% = 25.96% error |(72818.4499m3 - 73430.348m3)| / 73430.348m3 * 100% = 0.83%7. the percent error, which of the three dimensions will have the greatest impact on the uncertainty of the volume? Justify your answer.Out of the three dimensions the height would have the greatest impact on the uncertainty of the volume because the height is must greater than the length and width so it would be more likely tohave a greater impact if the number was incorrect. When we were measuring the height, it was more likely that the height was off by a greater number compared to both width and length since we didnt account for the attic of the library, basement and other unknown floors.8. What does rand() do? Feel free to use the internet to look up this function. rand() returns a random number that is greater than or equal to 0 and less than 19. What does NORMINV() do? To help you understand how this function works, it may be helpful to adjust the values of the average and standard deviation. Feel free to use the internet to look this up as well.NORMINV() calculates the inverse of the Cumulative Normal Distribution Function for a supplied value of x, and a supplied distribution mean & standard deviation.10. What is the mean and standard deviation of the volume of the library calculated using the spreadsheet? Attach a copy of your spreadsheet to your lab report. Mean:73378.232m3Standard deviation:2087.563m3 11. Compare your uncertainty measured with this technique to the educated guess you made in question 4. Was your estimate of the uncertainty too high? Too low? Just right? Our estimate of uncertainty was too low. We expected to be off by about 10,000 m3 while in reality, the difference was about 25,000 m3.12. Calculate the percent error on the volume, and compare this value to the percent error of the dimensions. Is the percent error equal to the sum of the percent error or the percent errors of each dimension multiplied together?Percent error of volume: 0.769% Percent error of length: 0.0135% Percent error of width: 0.0075% Percent error of length:0.064%sum of the errors13. Why do you need to look at percent errors when comparing the volume with its other dimensions?You need to look at other percent errors when comparing the volume with its other dimensions because it tells you how far the calculation is from the actual answer and lets you compare to the other dimensions and you would be able to tell which dimension is causing the percent error to increase or decrease. 14. Make an educated guess on how your measured volume compares to the actual volume ofthe library. Do you think it will be higher or lower? Explain your reasoning.We expect our educated guess to be much lower than the actual volume of the library. We expected this because it was very difficult to come up with a method to measure the height. We decided to measure one floor from inside the building, but that number did not account for the much larger first floor and basement, making our estimate lower than the actual volume.15. Evaluate your method of measuring the volume of the library. What are the strengths and weaknesses of your method?A strength of our method was being able to measure the outside of the library with the small square tiles as a reference. The tiles outside were easy to measure and 55 tiles fit the outline of the library perfectly for both the width and the length. So we don’t believe that our calculations for the width and the length were too far off from the actual. A strength for measuring the library was measuring a floor of the library because we know that the library has 26 floors so that was probably the best option in our case. A weakness of our method when counting the width and length of the library would probably be not accounting for the bricks that make up the library or not considering that the library is not a perfect square/rectangle. Another weakness in our method for measuring the height of the librarywould be not taking the basement of the library into account and we only measured one floor of the library which could also be a weakness. We also do not know if all the floors in the library are of the same height or if there are extra
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