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Grades 11-12 Video Solutions 2023
2023_11-12_18
2023_11-12_18
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Video Transcription
Problem number 18. Noah drew a closed path on a rectangular prism. Which net could show his path? So here the choices do matter and we're gonna have to work through each choice to see if any of these paths are possible. Obviously one of them is because there's no answer that says none of the above. So each net it can be uniquely folded into a solid rectangular prism. We just have to do that in our heads and draw the magenta lines or black lines if you were working with a pen wherever each path would lead if the nets were folding. So here's choice A. Choice A if we were to draw the magenta lines just visualizing this prism in our heads we see that there is a problem right here and we don't have a closed path. Choice B right here and right here we don't have closed path. Choice C right here and right here we don't have a closed path. Now at choice D though we do have closed paths everywhere. Now on these types of questions if you're short on time you would just pick choice D and move on. But a lot of times if you have just like another 30 seconds it doesn't hurt to check the other choices because it's possible you made a mistake. So if choice E doesn't work then we're extra confident that we didn't do anything wrong because four of our choices didn't work and only one of them did. So let's check choice E and sure enough we see that right here and right here choice C is not a closed path. So the correct answer for this one is going to be D.
Video Summary
The problem involves determining which net of a rectangular prism allows for a closed path drawn on its surface. Each option must be visualized as a folded prism to check if the path closes. The choices A, B, C, and E all have issues with incomplete paths when visualizing the prism, whereas choice D successfully forms a closed path on the prism surface. The solution advises selecting choice D, and validating by checking all options can increase confidence in the answer. Thus, choice D is confirmed as the correct net that exhibits a closed path.
Keywords
rectangular prism
closed path
net visualization
choice D
solution validation
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