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POTM 5 - Teams 1 - 4 The Earth’s Circumference A steel band is placed around the earth, snugly fit at the equator. (The equator is approximately 25,000 miles in circumference.) This band is cut, and a 36 inch piece of string is added to the steel band. This new circular band is placed around the earth, hovering above the earth’s surface, with its center being the center of the earth. A gap is created between the equator and this circular band.

How wide is this gap?

1 -Hello Earthlings, I think the answer is about 5.7295779513082320876798154814105 inches c=pi*D Get the radius by dividing 2 to both of the diameter, 0.5(25000/pi) and 0.5(25000+3ft/5240)/pi. Next subtract them, 0.5(132000003)/pi)-0.5(132000000/pi)=0.5(3/pi)=(0.5)0.95492965855137201461330258023509= 0.47746482927568600730665129011754ft.= 5.7295779513082320876798154814105 inches I found a flaw in my first one and corrected it, i got 4.7 ft. originally, off by a decimal point.
 * __Class Member Contributions__**

2 //-**How did you get this answer because the answer I got was much less and if the circumference is always longer than the diameter than shouldnt the answer be less than 3 feet? This could be wrong but I converted the miles to feet and since 1 mile =5280 feet I multiplied 25000 by 5280. This gave me 132,000,000 as the circumference of the Earth in feet. If X equals the gap then this formula (132,000,003/pi)-(132,000,000/pi) = 2X should solve for X. From this I got .477465 feet which is equal to 5.72958 inches. This number is unfriendly but the process seems sound. Any Comments?**// My old post is in bold and i somewhat got 5.7 but not with the decimals. The new math came out even and friendly and I endorse it. What I did was take the two feet numbers and instead of putting them in the equation I divided them by pi first and seperatly. This gave me 42016904.98 for the smaller and 42016905.93 for the larger. The diffrence of these is .95 ft Now I needed the radius so i divided by two this gave me .475 ft. I multiplyed this by 12 and got 5.7 inches on the dot. I think this cleaner answer can be used because there is a higher chance of flaws in the older method which could lead to a more likely incorrect answer. Any Comments? I am filling in the answer if anyone strongly disagrees they can post thier complaint by 6 pm on thursday the 24 otherwise we wil not achieve a strong enough answer. in the justifcation I added the work by team member 1 and the picture by team member 15 to allow for what I thought were the two most important contributions. i also added a simple logic check from myself to the justifacation. 3- I understand the formulas and the math. I also am going to try to double check your work, even though you got the same answer.
 * __In response to team member 5__** **__wondering why team member 1 multipied by pi. Pi is the ratio of the circumfrence to the diameter in any circle. Due to this the circumfrence can be reached by multiplying the diameter with pi and the diameter can be reached by having the circumfrence divided by pi. I see no error in Team member number ones math. Please show me if I missed something.__**

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4-Wh y would you divide both sides by the diameter? Anyway I tried the problem and my answer was way different than person number 1's person number one I did the problem on tuesday night and I actually agree with your answer of 5.72958. ===== 5- Why would you multiply it by pi team member 1? Ok now I understand however when you multiply by pi do you multiply by the pi button or just 3.14. I understand the formula and everything. 6- I agree with student number two, their process was pretty similar to what I did and i agree that the answer is about 5.7 inches. 7 -Ok, so first i converted miles into inches so we could compare the 2 circumferences when we added the 36 inch piece of string. I also drew out a picture of the 2 bands and noticed that to find the gap i would need the radius of each circle. I saw that 1 mile=63360 inches. Therefore, 25000 miles=1584000000 inches, that equals the circumference at the equator. Next, I did a second equation adding 36 inches to the circumference at the equator which then equaled 1584000036 which is the circumference plus the new piece of string. Then, I tried to find how I find the difference between the gap. I looked online to find a formula. c/d=pi. Once we find the diameter we can divide it by 2 to find the radius of each. We know the circumference of each band and we know that pi=3.14159...so then i did the math. The diameter for the first band is 504203285.6 inches and then the radius would be 252101642.8 inches. The new band the diameter is 504203297.1 and the radius would be 252101648.8 inches. Then, I subtracted the smaller radius from the bigger radius and got 5.7 inches. the gap is 5.7 inches wide. 8- I think that our final answer of 5.7 is perfect. Team member 1 and 2 are off to a good start. 9- 10-I think the answer is right and I will check the math of persons one and two. 11- 12 13- I do not understand this promblem can someone explain how you knew what to do. 14 - i agree with # 1 15 - I drew a picture to help us understand it. (: 16 -

 **// 1 point //**** State ** what the problem is looking for. The promblem is looking for how wide the gap between the equator and the new band. The gap between the equator and the new metal band is about 5.7 inches wide. First we took the original circumfrence and set it to the form of feet. Then we took the length of the piece of string and set to feet while adding to the circumfrence. We took the new circumfrence and the original circumfrence and divided them by pi. We then subtracted the original diameter from the new diameter. This gave us twice the gap. We divided the new difffrence by 2 and we converted the new number into inches. This gave us our answer of about 5.7 inches.
 * // 2 points //**** Answer ** the problem correctly.
 * // 5 points //**** Explain the process ** you used to solve the problem.

I think the answer is about 5.7295779513082320876798154814105 inches c=pi*D Get the radius by dividing 2 to both of the diameter, 0.5(25000/pi) and 0.5(25000+3ft/5240)/pi. Next subtract them, 0.5(132000003)/pi)-0.5(132000000/pi)=0.5(3/pi)=(0.5)0.95492965855137201461330258023509= 0.47746482927568600730665129011754ft.= 5.7295779513082320876798154814105 inches
 * // 2 points //**** Justify ** your answer. Type in the content of your page here.

A logic justifacation is that since pi = the ratio of a circumfrence to a diameter in a circle then 3 feet added to the circumfrence of 132,000,000 ft should make a change so minial to the point of a few inches. This logic supports the math previously stated due to the fact that the gap is a gap of a few inches.