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Boxes and Boxes and Boxes
Below you see an open box.
The result of cutting along the four darkened edges and then flattening the box is shown below.
You will follow the link below to open a grid. Save the grid to your documents - then open it in paint. You will draw all the nets that will fold up into different open boxes with a volume of 8 cubic units. Be sure to label your drawings with numbers that show the length, width, and height for each box. (Each square on the grid has a side of length 1 unit.) Be sure to show or explain how you know your net will create a box with a volume of 8 cubic units. The dimensions alone are not enough to be concidered proof. Be sure to also include proof that you have all the boxes you make for the given volume.
Click Here for Grid Paper
When you are finished paste your pictures into a word document along with your explaination and e-mail it to me at mathclasshonors@yahoo.com You can not just click on the address, you will need to open your email and copy and paste this address in your "To" line. Then attach your word document. DO NOT cut and paste your work in the body of the email.
Ms. Leckman
A.B.
ReplyDelete1. ALL lockers that are square numbers will be left open: 1, 4, 9, 16, 20, 36, 49, 64, 81 and 100.
First, I was looking to see how many factors each locker number had, and I thought that if the locker # had an odd number of factors, then it’d be open. As I was looking at the numbers I had found, I realized that they were all square numbers. So, I double checked by going through all of the times these lockers were touched and it turned out that I was correct.
2. The lockers that will be touched only TWICE are all prime numbers, which is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
This is because all prime numbers have two factors, which means that they’ll be touched exactly twice.