It was a bad week for me on KA. I only got through two exercises, both of which were fairly easy, meaning I should have got WAY more accomplished than I did. ☹️ I started the unit test on Sunday, got the second question wrong because I wasn’t paying attention, and then decided to wait until next week to restart it. The exercises I worked through weren’t just easy, they were also somewhat enjoyable (as far as learning math goes, anyways), so I REALLY don’t have much of an excuse not to have made more progress. Except that’s not exactly true… My excuse is that things happened this week that may lead to the biggest change in my life in the past nine years. Given that life may be completely different in the next few weeks, what’s been going on personally has taken up a lot of my thoughts/energy/focus. Anyways, I did take notes on six questions between the two exercises and the unit test, so here they are:

Exercise 1 – Volume of Prisms and Pyramids

Question 1

This exercise was the third and final exercise from the section Cavalieri’s Method and Dissection Methods, the section I was working on at the end of last week. Really, this question is pretty simple and just asks you to determine the volume of a cylinder which I figured out that the formula would be πr² * h. The only tricky part was that the cylinder was slanted (which I assume is what the word “oblique” means in the statement). But given Cavalieri’s principle—see my last post for what it is—I determined that fact that this particular cylinder was slanted was irrelevant when using the volume formula since width along each ‘slice’ of the cylinder would be the same regardless of if it was slanted or not. 

Question 2

This question was in the same exercise, but I don’t really know why. It didn’t require me to use Cavalieri’s principle. 🤔 As you can see, I just needed to calculate the volume of the half-cylinder which was simple.

Exercise 2 – Apply Volume of Solids

Question 3

This question was from the last exercise in the unit that I needed to get through from a section titled Volume and Surface Area. It took me about 30 seconds of thinking to figure out that I needed to calculate the volume of the cylinder with a height of 20cm and then divide the volume by the rate at which the pool was being filled by water. Pretty straightforward math, and honestly pretty straightforward logic to figure out, but it was kind of a fun question and a throwback to easier/more-fun math which was nice. I also remember being very confused by multiplying/dividing units like cm² and cm³ and this time it was very clear to me where certain units would cancel out and why they’d cancel, which was very satisfying. ☺️

Question 4

I had gotten a question similar to this one wrong on my first attempt which made me need to restart the unit test. So, I ended up getting this question correct since I already knew what needed to be done. (To be fair, I ‘should’ have gotten it correct the first time but just made a careless mistake. 😠) That said, I did need to Google the formula for the volume of the sphere. It also took me a bit of thinking to figure out the steps I needed to go through to solve the question, then a few minutes more to actually get to the solution, so it was pretty satisfying when I got this one correct.

Unit Test – Solid Geometry

I literally have five minutes to write the rest of this post, and since I didn’t actually finish the unit test, I’m not going to explain the questions below. I should mention that I got the first question correct and the second one wrong. (Again, another careless mistake on the second question.) I’ll go into more detail about this unit test next week!

Question 5

Question 6

And that was it for this week. Once again, not a very productive week, but progress nonetheless. I have a feeling I may have much more time to put into KA beginning soon, so I’m hoping my progress will double or triple in the coming weeks and I can finally finish this off. I just looked at the remaining courses I need to bring up to 100% and there are seven of them which sounds like a lot, but of those seven, the course with the lowest percent is Algebra 2 at 96%. So, if I can get back to putting in 5-10 hours on KA per week, I don’t think it’s going to take me too long to get it all done. Either way, sooner or later I’m going to FINALLY achieve this goal I set for myself 312 weeks ago. 😮‍💨 

(But hopefully it will be sooner rather than later.)