Regents Recap, August 2017: How Do You Explain that Two Things are Equal?
Sue believes these two cylinders from the August, 2017 New York Regents Geometry exam have equal volumes. Is Sue correct? Explain why.
Yes, Sue, you are correct: the two cylinders have equal volumes. I computed both volumes and clearly indicated that they are the same. Take a look!
Wait. Why did I only get half-credit? What’s the problem, Sue? You don’t think this is an “explanation”? The two volumes are equal. The explanation for why they are equal is that I computed both volumes and got the same number. I don’t know of any better explanation for two things being equal than that.
What’s that? You wanted me to say “Cavalieri’s Principle”? But if I compute the two volumes and show that they are equal, why would I need to say they are equal because of some other reason? Oh, never mind, Sue. See you in Algebra 2.