The sears tower in Chicago is 1,454 feet high. suppose you take a sheet of paper and fold it once in half, than fold it in half again,and keep folding it over and over again. How many times would you have to fold it to create a piece of paper that is higher than the sears tower?
How thick is the paper?
Thickness(2)^n = 1454 feet
(That must be one super-big piece of paper!)
To determine how many times you would have to fold a sheet of paper to create a piece higher than the Sears Tower, we need to calculate the height of the folded paper after each fold.
Let's assume the thickness of a sheet of paper is approximately 0.1 mm or 0.00394 inches.
Initially, the paper has a height of 0.00394 inches. After the first fold, the height doubles to 2 times 0.00394 inches, which is 0.00787 inches.
With each subsequent fold, the height doubles. So, after the second fold, the height becomes 2 times 0.00787 inches, which is 0.01574 inches. After the third fold, the height is 2 times 0.01574 inches, which is 0.03148 inches.
We can continue this pattern to find the number of folds required.
0.00394 inches -> 1 fold -> 0.00787 inches
0.00787 inches -> 2 folds -> 0.01574 inches
0.01574 inches -> 3 folds -> 0.03148 inches
0.03148 inches -> 4 folds -> 0.06296 inches
0.06296 inches -> 5 folds -> 0.12592 inches
0.12592 inches -> 6 folds -> 0.25184 inches
0.25184 inches -> 7 folds -> 0.50368 inches
0.50368 inches -> 8 folds -> 1.00736 inches
1.00736 inches -> 9 folds -> 2.01472 inches
2.01472 inches -> 10 folds -> 4.02944 inches
4.02944 inches -> 11 folds -> 8.05888 inches
8.05888 inches -> 12 folds -> 16.11776 inches
16.11776 inches -> 13 folds -> 32.23552 inches
32.23552 inches -> 14 folds -> 64.47104 inches
64.47104 inches -> 15 folds -> 128.94208 inches
128.94208 inches -> 16 folds -> 257.88416 inches
257.88416 inches -> 17 folds -> 515.76832 inches
515.76832 inches -> 18 folds -> 1031.53664 inches
1031.53664 inches -> 19 folds -> 2063.07328 inches
2063.07328 inches -> 20 folds -> 4126.14656 inches
After 20 folds, the height of the paper is 4126.14656 inches or approximately 343.84554 feet, which is higher than the height of the Sears Tower.
Therefore, you would have to fold the paper 20 times to create a piece of paper higher than the Sears Tower.
To determine the number of folds required to create a piece of paper taller than the Sears Tower, we need to find out how many times the folded thickness of the paper doubles until it exceeds the height of the tower.
The thickness of a standard sheet of paper is approximately 0.0039 inches or 0.1 millimeters.
1. Convert the height of the Sears Tower to inches: 1,454 feet * 12 inches/foot = 17,448 inches.
2. Divide the height of the tower by the thickness of one folded paper: 17,448 inches / 0.0039 inches ≈ 4,476,923.
This calculation shows that the paper needs to be folded approximately 4,476,923 times to exceed the height of the Sears Tower.
Now, let's explain how we reached this answer:
1. Research the height of the Sears Tower: Use a search engine or visit reputable sources to find the official height of the Sears Tower, which is 1,454 feet.
2. Determine the thickness of a sheet of paper: Research the standard thickness of a sheet of paper. You can find this information on websites that provide details about paper measurements or consult books on printing and paper.
3. Calculate how many times the folded paper needs to double: Divide the height of the Sears Tower in inches by the thickness of one folded paper. Make sure your units of measurement match. This calculation will give you the number of times you need to fold the paper until it exceeds the tower's height.
4. Verify the answer: Ensure that your calculation is accurate by double-checking your units of measurement and the mathematical steps you used.
Remember, the answer might not be an exact number of folds, as this calculation assumes perfect folding and neglects factors like paper compression and limitations in practical folding techniques.