potm5

Shown on this page is our final response to POTM # 5. 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?

I got two methods created. It would be great to hear what someone from teams 5-8 has to offer. 1 - **//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.//** 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? Number 2: The question asks for the gap or the distance between two single points. Not both circles area diffrence.__** 2 - Number 14: Aren't we looking for the distance between the circumfrences and not the radi? 3 -I agree with number one and number 2 4 - ​Wait, haha, I know who number 14 is, but I agree with everyone else. Why did you find the difference between the two diameters? I liked what you did before: You used the diameters to find the radius then plugged that into the equation for area. Then, you subtracted the two areas... Wait, it seems like team member 1 has a different idea... OH! NOW I get team member 1's idea! At first, I didn't get it. But, I think that works too! I like your idea. I like team member 11's idea too! Wait, team member 11: Were you subtracting the radii to get the answer? Oh wait, haha, I've been like reading other people's thoughts and I keep coming back. Okay, anyway. I think what Team Member 19 did is the same as what Team Member 11 did. Am I right or no? Well, I think I like that way of doing it. 5 - 6 -I agree with number 1. Thanks for helping explain it further. :)
 * __Class Member Contributions__**
 * __ Number 14: You forgot to convert the diameter into the radius and you need to do this because the diameter is actually the length of 2 GAPS. This would give you 5.75 inches this number is slightly diffrent compared to mine so one of us probably messed a decimal digit or something like that.

7 - So, basically everyone's saying to subtract the smaller circumference from the larger circumference. and c= pi * diameter. And, then you solve everything else, converting the miles into inches and yeah...I was a little confused about the width part, but after reading number one's explanation i understand. Mostly. hehe. :D 8 - O.K... so this is all pretty confusing, and I will try to share what I did as best as I can: WOW OKAY THIS IS A REALLY HUGE PICTURE!!!!! Sorry that I took up so much space, I hope nobody minds :) !!! I hope the diagram is understandable, but uhm, first I found the circumference of both circles. At the top, you can see that I converted the miles to inches, and below I found the circumferences using pi times diameter (the 25,000 mi converted to inches). I decided that the next step was to find the area of both circles, but this is the part that I really have trouble with. It is so hard to multiply huge numbers!!! After we find the areas though, I think that we should subtract the smaller from the larger to get the space in between. But then we have to find the width of the space... my head was too spinny to understand the rest. Does anyone have any ideas? Number one had a great idea with the miles to feet- 36 inches is 3 feet!!!! Great observation!I think that if the numbers werent so big, this would be easier. I think number one's got it, though... 9 - Number one pretty much sums it all up! And I agree with number 2. 10 - 11 -5.7295779513082320876798154814105 inches c=pi*D Find the radius by dividing 2 to both 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 __**
==] = 12 - 13 - I agree that the answer to this problem is 5.7. I really liked number one's aproach because they were able to get 5.7 on the dot. However when I did this problem I originally got .477465 feet and then converted that to 5.72958 inches. I think the way number one did it was more smooth and flawless. 14 - I converted the 25,000 mile circumference into 1583999669.2926407 inches. When I added the 36 inches I got 1583999705.2926 inches for the circumference of the new steel band with the string.​ I put each of the circumferences into the equation, C =(pi) d, "Cherry Pie's Delicious" :], to solve for the diameters. The diameter for the original steel band was 504202754.4 inches. The diameter for the new steel band was 504202765.9 inches. Then I found the difference between the two diameters which was 11.5 inches. So maybe the gap is 11.5 inches? It could be wrong because those are some fairly large numbers. I think it makes sense though. What do you think? :] 15 - 16 - I agree with number 1. At first I tried a different approach but I got an unfriendly number with alot of decimals. I didn't think that was right, so I tried team member 1's approach. I think that was eaiser and it made more sense. I also got 5.7 inches as my answer and I'm pretty sure that's right. :) 17 - 18 - 19 -I agree with all of the people who said that the final answer is 5.7 inches. I showed how I got this in the last round with all the numbers. I converted the miles into inches for the circumference and the new one with the added piece of string. Then, I found a formula which was circumference over diameter equals pi. So, now I could find the diameter of each. I also drew a picture with a dot in the center and the 2 bands. In order to find the gap, I would have to find the radius of each band and the difference would be the gap. Once I put the numbers into the equation and found the 2 diameters I divided them both in 2. When I subtracted the smaller radius from the larger radius, I found out that the gap is 5.7 inches wide. There it is. 20 - 21 - i agree with whoever said 5.7 inches :] 22 - 23 - 24 - 25 - 26 - 27 - 28 -

 **// 1 point //**** State ** what the problem is looking for. How wide the gap between the circular band and equator is. The gap is 5.7inches wide.
 * // 2 points //**** Answer ** the problem correctly.
 * // 5 points //**** Explain the process ** you used to solve the problem.


 * // 2 points //**** Justify ** your answer. Type in the content of your page here.