Take-Home Assessment for Patterns
Problem Statement- There is a cube that is 5 inches long on every side the large cube is made up of 1 inch smaller cubes, and each smaller cube is 1 inch on every side. Someone paints the outside of the cube and the paint doesn't seep to the inside. How many of the smaller cubes have any paint on them at all. How many of the smaller cubes have just one face painted? How many of the smaller cubes have two faces painted. Answer the question for three, four, five, and six.
Process- First I knew I needed to figure out how many cubes were in the entire cube. This would be the volume of the cube. In order to find the volume you take the length times width times height. 5 * 5 * 5 = 125.
Then I needed to find out how many of the smaller cubes had any paint on them at all. I started out by using a drawn cube to help me organize and count. I started with the corners of the cube to see how many of the corners were painted. There are 8 corners. Then I counted the edges but didn't include the corners because I had already counted them. There were 30 squares around the edges of the cube all together. Lastly I needed to find the faces that were not part of the edges of or the corners. There are 9 squares sides that are not in the edges or corners on one side of the cube and since there are 6 sides you would multiple 6 * 9 = 54.Then to get the total amount of squares with paint on them you would add 8 + 30 + 54= 92.
In order to find the amount of cubes with one face painted you would take the 54 you got from all the squares in the middle because of those ones were the ones with only one side painted.
In order to get all the amount of cubes with two faces painted you would take the cubes on the edge that were not the corners because those were the ones that only have two faces painted. Which was 30.
For three, four, five, and, six faces you would get 0 for all of them except three because four, five, and six faces wouldn't...
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