We came to be supportive and to answer any questions and help build a strong relationship with the school and with what we're doing down in the woods. So next we've been on the consent agenda and I know there are just a lot of fantastic, fantastic work. Thank everyone for it. It's great, but it doesn't include... If we have to show... I thought everything else on top of that is essentially a good guess here on our behalf. That's all this is. Here's a full of the policy changes. Not put on the agenda, but yes, but we do plan it if you want to. Thank you for your discussion. Thanks everyone for coming. We do want to talk about the first walk and also the sense that we have it around. I said around a lot of things. One, I hear you on the volume of the first walk. I've heard things about it. I know it's a program. I've found, at least for the title of this program, a good rhythm to have. As a district, we understand there has been a change in what we've been having in the past. It's clear that we have never had a policy. So what was occurring in the past should have technically been occurring too. We also, at least not from our knowledge, including not just the attendance thing, but other questions that I think should come up around that, such as who's responsible for ensuring that the class time is made. What do you do if it's not working for you? What do you do if it's not working for you? Right now, it's a factor available to the families that can afford to send a piece of report both from financial position, but also from getting them their transportation, which is just fairness and equity issues. Why just... The block is great, and it does great programming, but it's outdoor education, which might not be a bit of a kid. What about parents? So I think there's a lot of unanswered questions about the burden of district that we have in Russell. And then there's the legal questions too. The state law requires that students be in class for their approved education programs pretty clearly defined. Emergency, and I haven't dealt with what emergency means, but our district goes 178 days. So those 3x per day is confused. I'm trying to get some space on that. The idea here is to prevent insurance. Yes. That's the whole point. So if kids running around can't, so if parents take the child out of town, they'll give her a super-tent. The North Branch would not call them. My wife took my daughters to Costa Rica. Absolutely excused. 10 days. No less than. I'm just throwing it out there as a... I don't really have a... There are many adults, that's what I'm saying. I'm just saying I don't think there's any law against what... I mean, that is something we should... I don't think we should... I think we can just legislate for insurance and some case law and our apps for those. Yeah, it's a valid question. I mean, I was reading in the absence of a doubt. Yeah, not... That's not what it says. Not when we'll see what it will bring. Because one failure residents wouldn't be able to participate in the North Branch data center, and technically a Roxbury child would be able to go to the North Branch data center and give us that discussion. Well, that's a question like, which town is in the town of Jones? Is it the town of District? It doesn't. Excuse me. We need to create a substandard ourselves by which, you know, we'd delegate that to the superintendent. Right. So we just need to say, oh, well, I guess we... That's why we wanted to get clarity from Ginger about it. Right. And so it may be... We also need to... I mean, my understanding is, but it is a way for... So, my understanding is, and I would not... What happens then is, and we... My understanding is that they only basically will check in with the district and say, is this creating... If the district says, you know, the child's name's right, the child's driving, that's basically the end of the... Is an issue, then, you know, if we counted these as excuses, I think we'd want, as a policy matter, some sort of internal monitor.  So I think they have to be mindful of... But do you do that for the families? But do all families or anything like that? Some sort of a check-in. If you check the principal, everybody would agree, no, you know, these kids are... These kids are up to speed, they're good to go, go. Yeah, you know? Because most of the kids do have a lot of vacation outside. Well, I think you should all talk about this. I mean... But there's a legal mechanism for homes. I mean, I think... And there is for this, arguably. Arguably. But I think when we're asking... I mean, I think we all want to give as many kids as possible. We have school five days a week for a reason. And, you know, and if people say, well, when career four works for my kid, it'd be better.  I do understand about it, but what we're really debating is... You know, families... You know, families of limited means who can't afford to take their kids out there are not the families we're looking for. And I think if we're going to sanction it as a district, we should do so in a way that allows everyone to access that opportunity. Right. But I'm not sure there's any difference between this. They're out of town. This district... Yeah, I'll say it's excused. I mean, I think... We can... Well, doesn't one have to go out of town? That's clearly one of the two standards that the district be allowed to, but aren't required to, to excuse. Yeah, and this is made for that reason. And I'm saying that that might be a good thing to be excused also. But... And I think there's a substantive difference, too, between a one-time trial. Regular absences... I'm advocating for making it an excused people on a family vacation when you're in school. I'm okay with that.  I'm trying to be consistent. I get... I agree there's a class issue, but I don't understand. I also agree that it's right. That's just, that's unnecessary. School exists for a reason. Your role in a public education... I'm sorry that I got distracted from the misrivity and discussion. And you can go to a whole school on many courses. Isn't there... You can take advantage of four, four content areas. Am I right on that? And still be considered homeschool? Yeah. I don't remember off the top of my head. There's some limit to what you have to do. It used to be... It used to have to have six to be considered full-time to qualify to play in extracurriculars. But I think that that number is gone by the wayside a little too in the last few years with flexible pathways. People not keyed in on that. It's possible to be responsible for themselves immediately upon their grade, right? Because they sort of, when you shift to, when you've got an economy, and it's really hard for those people. And that's why it's a lot of problems. It's a lot of problems, right? Right by the district. So flexible pathways is improved. But a kid's next... That's actually... In general, too, is a problem. It's very different. So... Yeah. It's really hard to use. I would... I guess what I would like out of this is whether we want to take further action. We wanted the four content areas. Which is the... Are you saying that if... If I take my kids out during the school year, I should get an uninscubed... They're getting uninscubed to take them to some place that actually... That's actually really assistive and educational. They're round out, and I'll enter a couple of days around this idea that to be consistent, being very formal about the fact that now we are staff make this up. So maybe that is an uninscuse. I just... I just want to be... They're doing... They think it's really assisting in the weekly class work. I know that when I did it with my other daughter, it was essential. It kept her from going insane in the school, in third grade. And to go once who we get wasn't hurtful. It was somewhere else. That was really valuable to get her focused. It was a really good student the other four days. If there had been any excuse, I wouldn't care. We're not to sort them down the line, but the four kids you reported to took an incision. I mean, so the teachers, those are in the handbook? That's what I'm talking about. They're in the handbook. What is listed in the handbook? But I guess what it does for you is... Right, I still chair it. To a sense, the more of those uninscused you accumulate, the better rather than a whole bunch of excuses. Yeah, well, that's because if they're excused, you're not keeping track of it. Right. Yeah, exactly. That's kind of what I'm saying. I think the principal is not pleasant to receive, but it's an automatic check that I think we have to put in place. And we have to put in place asking all these questions to act as the feminist program. And I actually... I like the idea of... There's a move toward equity, is what it is. No, I'm just going to... No, I'm just going to... No, I'm just going to... No, I'm just going to... I'm just going to... I'm just going to... I'm just going to... Then at 10 of those, someone's like, this literally isn't good for this kid that this family keeps going. They're not really succeeding, you know, or it's disruptive, or it's creating too much pressure on the teacher, or, you know, there's, like, all of a sudden this is going to happen. So the permission for the visitor that's different than what would be more restrictive than the law. The law is saying, do you want to excuse out-of-town meetings? So what happens... What do you know? It doesn't... Do you want me to talk about it? Sure. Okay. Yeah. So, um... You've probably had a few words. And you're following the pamphlet, right? Yeah. Yes. So students come to me constantly. Sometimes I feel like the only purpose I serve is to sign their find-outs. But at least I'm signing something. And I always check unexcused when students are going to Thailand, or because they're going on vacation so it's unexcused. And we accommodate them because if a student is going to be gone for an extended period of time, which is why this is coming up, that's different to me. So you're going to be gone for a month or two months. Then we've got to slow down and say, wait a second. Like, is this reasonable to put on us? But if a student is going to be gone for a couple of days, then we say, check in with your teacher, see what you're going to miss. You're responsible for the work that you miss. You're going to make it up. But it's unexcused. The question then is it going to trigger an emergency letter? And the answer is that technically, yes. And there are so many absences, which is a plea that I make in my opening letter to families each year. Please, please come to school. Please come to school. Please plan your vacations carefully so that it's not, I think there's an element of respect about the challenge that poses for teachers in schools when people are just gone all the time and you're trying to hold a class and half the kids are there because people are out doing good things, but they're not there. So, yes, we, I ask that of families in the summer letter, please come to school. And when people have good reasons for not being there, we do our best to work with them and accommodate them. And I do think it's different in high school. There are students that are constantly engaged in really good stuff that takes them out of school and they're older and they're at a different developmental level. And so they are navigating the executive functioning skills necessary to plan ahead and to make up things. And I think that is good for them in some ways. But when the piles of unexcused absences come in for this or that, there is an editing process, right? To say like, does it make sense to go to truancy court for this family or not, right? Like, is there a concern that we have? You talked about the trigger and I'm sorry, but I'm not concerned. You know, if they have good grades, I mean, it's not just like, oh, we like them. It's like, they're doing fine in school, but if they're not and we are concerned, then it is a piece of the puzzle to try to support a family. So, I mean, I think there's an element of practicality that does come up for us with truancy. And the other thing that, I mean, I think is worth saying and maybe you know this and I feel like you kicked it around a little bit, but truancy for schools a lot of times is very much a dead end. It's a ton of work with almost nothing on the other side. So, it means that oftentimes it's not taken up by any community partners, particularly at the secondary level. I mean, you know, that's where most of my experience is. And so, if you have a 16 or 17 year old that's not coming to school, you file truancy, thinking that you're handed the baton to DCF or or sort of practices, Washington County Mental Health, the baton is not quickly or easily taken. Right? It's very low on the scale. And in fact, sometimes they just say we're not. So then, as a school, we have to make a decision about how much energy are we going to invest in pursuing that path or are we going to put our energy into re-engaging the student. So, I mean, I know that that's not quite the discussion about missing a day of school in second grade, but... Yeah, yeah. Can I make a radical suggestion? I actually suggest that we kind of trust and make sure that families that want to do this that there's encouragement or an encouragement of it could simply check and so families know what they're prepared for and when those letters come, it's not a scary thing. Steve, I think our sister was unexcused. Actually, there's a third option that teachers can pull down and it's called planned absence. And I don't know how that one gets recorded. I think that's up to five days. That's under the time. There's less discussion for emergencies. We're clear that vacations are school. Parents... I'm sure that's going to tell you that. There's going to be more on that trip that we're in school at. Which is true, but... It's different, right? Are you seeing an entire coverage? Is this the questions that are already on that list? So question number one if you could... That's the Agency of Education. Yeah. Yeah. We're talking about... My question's actually about the agenda because I apologize but I did not understand what the consent agenda means and I know that Hope and Emma aren't written on the agenda. So I'm wondering if you could just say what the agenda is moving forward and I think the public comment section is done. Yes. So... Oops. So we have Hope and Emma who give the student update which is actually kind of very exciting. I actually didn't know what they were doing on the agenda but I just... Can you... I think I even missed the moment where the consent agenda might have been approved. I saw things get pulled off of it but not... So there's... The policy that the board is adopting for diversity, equity and inclusion I will just maybe email my comments to the board at some later date like this evening. Thank you. Oh, thank you. Sorry. Well, did... Did I miss the moment? I totally missed them. I totally... I was waiting for that. We're not talking to you so it doesn't happen. Yeah. So... So just for future... For future... Thank you. So... So we have the public comment period just kind of where you can comment on anything that's on the agenda. The consent agenda are things that we have discussed and are things that need... don't need discussion that we're ready to approve that discussion. So the reason that we didn't discuss the first equity inclusion is that course and so we're just sort of point where like the board discussion... That's good. Yeah. I'm glad you said that. Okay. Good. I just didn't... I missed it. I was like, so it was just everything there without discussing it. Yeah. Didn't know that. Sorry. Okay. It's okay. I learned a lot of things about a school board meeting. So... I'm not just one. I would say that... I would give the motion... Oh, someone's over here. I'm not... I'm not... I'm not... I'm not... I'm not... I'm not... I'm not... I'm not... I'm not... I'm not... I'm not... Well... I must call and bring the call. That's not what is this. It's my wonderful solace... From a諘ou... You shall be our accomplice. They don't need anyone. I'm not understanding... Back in. I opened up his experience. But our fundamental concern is always whether the kids are competing in school, or more so. Yeah, it's a small number of students, probably larger at the high school as kids get older, that just like, yeah, I'm not going. It's almost always, and we should not say always, but it's frequently connected to many other issues. Digital addiction is the thing that I'm most keen in on. I think that when I was a kid, if I played cookie, that meant that I was watching Days of Our Lives, which I did not particularly care for. And if a student plays cookie now, it's incredible what their options are. So, digital addiction, I believe it's very real and effects of it. So, oftentimes, again, this is like a little bit of a soapbox, but I'll zip it in a second. Oftentimes, we see this huge spike nationally and here in depression and anxiety diagnosis. And I think that the digital addiction piece is really connected to that. So, oftentimes, students that have school refusal also have a diagnosis of depression and anxiety. And I think it's all sort of mixed in there with digital addiction and nerves about social interactions and pressure, and it's all mixed in, which is really what Lisa Noss's Rolling Fellowship was about. It was about building a culture of wellness, risk-taking, and resilience. I agree with you, Michelle, that it does sort of come down to the performance, especially as we struggle with truancy not having many tools to utilize with that, except the stark reality of, well, now you didn't earn efficiency in this, so you're not moving on. And my, at the secondary level, that gets very real. It's actually also thinking about... I can't say that I am saying that I'm going to a conference on Monday and Tuesday next week. That I'm also an excuseer of... And the first student celebration that I'm going to ask, and it's for the New England... No, it's just serious. No, it's serious. And they always, recently, maybe a year ago, got a bond approved that isn't even... Oh, it is very attentional. It's a whole separate system. So moving on, I actually think we can do this. In terms of port planning, we want to go so digital addiction. We're not going to bite off in one half day, but it's, I'm increasingly hearing it from the community, from a variety of angles. You know, some education and then something that we want to kind of continue to have a subject that we talk about, examine our policies around it. This is putting a lot on you, but kind of guide us into what's a chunk that makes sense to go first on. And then to solve those problems is more than a one-year strategy anyway. So it's really being reasonable. And every month since. You say us doing the board or the school. Which constantly meant the school. You can tell, maybe you could give us some background on where you see that we are. I don't think probably as board members we even all know, except through our kids' experience, at what point kids receive health education, what that consists of. And whether you or Mike see that as remotely adequate, I don't think anybody does. And how, you know, what plans you might have already for doing something about what are our options for doing something about it. And we have limited time. I'd throw Pam in that discussion. Absolutely. Yeah, definitely. That's where it should be done. So I had the candidates for the high school principalship do a writing task, and this exact topic was the writing task. Yeah. It was what would be your plan. So let's maybe start with education there. I think we could figure out what's happening. And some numbers too. What are, what do we know about? Some education about what we are doing. Yeah, but the behavior of our students, the addiction issues, mental health issues. I think there's new IRBS data. They just took it. So I'm not sure if it's out yet or not. Yeah, so actually the students at the middle school did a presentation. Was it this year's data though or last? No, it was last year's data. Last year's data. I mean, the one, it sometimes takes a, last time it took like two and a half years to get the data out. Yeah, I was going to say it, because did you all just take it like a week ago? Yeah. I mean, that's not, no, but some, the previous round did just come out. And for anyone who hasn't attended the parent, the kids' presentation at the middle school. They do a great job. They do. Yeah. So, so there's the scope question. Then there's the playing question. What's realistic in terms of time? My preference would actually be to get a lot of this done before the end of June. I think it's hard to coordinate around summer. And maybe we could pick up like last week of August or kind of first week of September, do another like more and die. And that sounds like a lot of the game due to extended sessions. Jim, I don't have, I don't remember and I probably should because we talked about the budget process policy a lot. Yes. What is our timeline because the directives, a lot of this stuff does align with how we went to impact budget for next year. Yes. So, whatever planning we do should do on these topics should be in alignment with that budget calendar. Yep. That's why it needs to be done this year. So, we're ready for. Is it typically our first, our full day meeting in June, I think is on the budget calendar as for discussing budget priorities. I'm looking at it right now. Are we going to squander our budget priority discussion talking about our children's health and welfare? No. It just says summer. Well, are you talking about. It says summer board superintendent leadership discussed budget priorities. And Jim, are you talking about doing this at a board meeting or are you talking about in addition to a board meeting? I was thinking of having two extended board meetings that we might shift like earlier into the day. Okay. And then doing a retreat that would be separate from a board meeting. So, you're suggesting that we do that in. Between now and June. Okay. Should we do a doodle poll to see, does that sound too ambitious to folks? And then we can send around a doodle poll to see which dates work best. I think it would probably be challenging if you're trying to include principles to have anything happen in June. Well, we could get. He wants it done by the June 1st board meeting. Yeah. Because you started when the staff still around. They don't have to state that. Yeah, it's perfect. I can pull principles for when we need. If we have the agenda set, we can pull principles for when we need them. And then they'll be fine with that. She says. They're going to love that. So why don't we send around some doodle polls and see which states work best. On the subject of scheduling, are we going to try to have two meetings in April? Or are we just going to skip? We never have a meeting, I think, in advance on the agenda during the spring break, which is almost always important. Now we have scheduled, at least I have down, April 3rd and April 10th. I think we did. April 10th. So the first two weeks in April, on Wednesday, we have a board meeting. It's going to be an unexcused absence. Yeah. Wait a minute. Why aren't you going to be here? Maybe I'll be excused. What time? I think it really is now. It's in Roxbury. Yeah, I may not be here. Oh, no. I think I will. So we better not extend the one on the 10th. If it's absent. If already. Yeah. That's in Roxbury, which has limited space for us to extend it. I'm just building it up. We'd be hanging out with that. Yeah, unless we want the keys. And I will be coming from the trouble. So maybe, for example, May 1st is a good one to extend. I can do it on doodle. That's who it is. Yeah. We don't have a. You don't have a ton to choose from. Okay. Okay. Great. Thank you. So we need the motion on. We need two motions on a very good position. We'll be in our detrimental to the board if we discuss the public. And then the second motion going to. So the first one. We have yet to post the language on that. Bridget is really good at this. I move that the board find that discussing contract negotiations and open session. With the board at a disadvantage. I'll second. I'll second that. Okay. I move that we enter executive session. I'll second. I'll do better. Hi. May I post? Okay. I must attend.


Hi, I'm Zor. Welcome to Unisor education. I would like to present to you an interesting problem related to the geometry of sphere. I would say it's kind of unexpected result. Let's put it this way. At least unexpected for me. I do suggest you to watch this lecture from the Unisor.com website because there are notes for any lecture and also problems are usually given with answers and sometimes with solutions. In this case I do have both answer and solution, but if you try to solve this problem yourself and just check against the answer, that would be much much more useful, obviously. And that's exactly what I'm suggesting you to do. Now if you cannot solve it, that's okay. The solution is on the website and I will present it in the lecture. But then try it maybe afterwards to do it just by yourself. All right, so the problem. Consider we have a sphere and a cylindrical hole is actually drilled inside that sphere. So the cylinder has the axis of symmetry going exactly through the center of a sphere. So it's a very symmetrical kind of thing. So the sphere was drilled in cylinder. Well, it's not actually a cylinder. It's a cylinder and two caps. That's what we are touching off from this from this field. Now what I would like to know is the volume of the remaining part. The remaining part it's like some kind of a ring without tops. Actually, you know what when you go to a good restaurant and they give you napkins in some kind of rings, the rings usually have shape of this type of thing. So Now to evaluate the volume of the remaining part, one would think that you really need lots of information. For instance, the radius of a sphere, right? Then the radius of a cylinder you are cutting through, the height of the cylinder. I mean there are certain parameters which must be specified. Now to our surprise, at least to my surprise, there is only one parameter which is actually sufficient to determine the volume of the remaining part after we drill this cylinder in. It's the H, the height of that cylinder. Apparently, if just this one parameter is given, without the radius of the sphere, without the radius of the cylinder, whatever, everything else seems to be just, you know, going, putting together a nice formula for the remaining volume after the drilling process. So just one parameter H is given, nothing else. Well, in theory, you might kind of understand it, that if you have a bigger sphere and this parameter is given, it probably means it should be a wider cylinder, something like this. If you have a bigger sphere, if you have just this length of the height, then it should be somewhere here. And the remaining part, although of a bigger radius, would have probably thinner walls, something like this. And the volume of the remaining part would be the same. So only one parameter H is given. All right, now let's go to the calculations. We have to get the formula and hopefully the formula will depend only on one parameter H. Now, I would like actually to specify radius of the sphere as capital R, radius of the cylinder as lowercase R. And since I needed the caps here, let's say the height of each cap is capital H here and there. Now, what do I know just looking at this picture? Well, first of all, obviously, I can relate capital R, lowercase R and H using the Pythagorean theorem, right? So it's R squared is equal to lowercase R squared plus half of the H squared. That's one equation, right? Another equation is, well, if you just drill through, well, if you imagine the axis, now, the axis of the sphere is basically two radiuses, right? And each radius is equal to half of the height of the cylinder plus height of the cap, right? So each radius is equal to half of the height of the cylinder, which is this one, or on the bottom it's this one, plus height of the cap. That's what I know. So if my unknown variables are radius of the sphere, radius of a cylinder and height of the cap, three unknown variables. I have only two equations. So obviously, I cannot determine them, knowing only the height of the cylinder H. But maybe it will not be necessary, because maybe in the formula, in the final formula, everything will just, you know, reduce itself and cancel itself, and only dependency on the lowercase H will remain in the formula. Alright, so now let's go to calculations. Well, the V, which is the volume of the remaining part after the drilling, is equal to volume of the sphere minus volume of the cylinder and minus two volumes of the caps. Right? Volume of the cylinder and two caps we take out. Okay, in terms of these variables, it's equal to volume of the sphere is four-third pi r cube minus volume of the cylinder is, if radius is lowercase r and the height is lowercase H, it's pi r square H and minus two volume of the cap is pi H square 3r minus H. That was in one of the previous lectures when I was talking about caps. Somehow, I remember this formula. Quite frankly, it's not an easy thing to remember, but I think that's what it is. So, alright, so we have all these dependencies on r, capital R, lowercase r and capital H, which we don't really know. However, I can use these dependencies, which I know about to basically use it here. So, what's the result if I will substitute? So, let's say I will leave just the capital H as unknown and r and r will be in terms of lowercase H and uppercase H. So, four-third pi, instead of r, I will put H plus H over 2 cube minus pi r square. Instead of r square, I will put capital R square minus H over 2 square and instead of r, I will put this. So, that would be r square, which is this, H plus H over 2 square minus, so that's r square, minus H over 2 square. That's r square and times H and minus 2 pi H square 3r minus H. So, 3r, it will be 3 capital H plus this. So, it would be minus H. So, it's 2 H plus 3 H over 2. Is that right? Well, we'll see. I mean, hopefully I didn't make a mistake. All right. Now, let me wipe out this and we will go off. All right, let's just, you know, open all the parentheses. Let me put it this way. Pi will go out and I will probably have... Oh, wait a moment, wait a moment. I think I have to divide it by three. Yeah, that's right. I said I remember the formula, but actually I did not. Now I remember because I have to have one-third, actually, also out. So, it's not just pi, it would be pi over 3, but I will have to multiply by 3 this middle part. So, I don't have 3 here. I don't have 3 there and what's remaining? Okay. 4 and this cube, right? So, it would be 4 H cube plus 3 H square times this H over 2 times 4, that's 12 divided by 2, 6. So, it's 6 H square H plus 3 H and this square. That would be 4. Okay. So, it would be 3 H H square and the cube would be H cube over 8. Now, this is 4. So, it's H cube over 2 minus minus. Now, this should be multiplied by 3 and divided by 3 because I put 3 in the denominator, right? So this is, well, obviously, H over 2 square will be reduced. So, I will have only H square plus 2 times H times H over 2 plus H H. So, it will be 3 H square minus 3 H, or K is H, right? And then H square over 4 and H square over 4 will be reduced. Minus. The last one. 4, okay, pi goes out and 3 goes out. So, it's 4 H cube and 3 H square H and I close. Now, it would be nice if everything would be just cancelling out. Okay. 4 H cube, 4 H cube. Okay. 6 H square H and 3 H square H. Now, I remember it was reduced. I missed something. Okay. How about this? H H square plus something is wrong here. I think I missed H here. Here. Yeah, this is the H. Of course. My fault. So, that would be H and would be H square. Of course. I forgot this H to multiply by this. Now, everything is cancelling out. 6 H square H minus 3 and minus 3. And 3 H H square and 3 H H square. You see, everything is cancelling out. And the only remaining part is pi H cube divided by 2 and 3, 6. So, the volume of the remaining part depends only on the H. And this is a very interesting formula actually. If instead of H, you would put, let's say, 2 X. What this formula would look like. It would be 8 over 6. So, it's 4 third pi X cube. Now, this is a formula for the volume of a sphere. So, basically what it says is that the remaining part would be exactly equal in volume to the volume of a sphere with the radius equal to half of the height of the cylinder. Strange. I don't know how it happens and why I cannot explain it, but I think it's an interesting observation. All right. Well, that's it. Now, I suggest you to do the following. If you did not do it yourself before the lecture, do it right now. Just go through all these calculations. It's very useful because it basically involves all the elements of the sphere. The volume of a sphere, the volume of the cap plus a cylinder also involved. And a couple of accurate calculations which you have to do, hopefully without making any mistakes. I made a little mistake here, but that's okay. And see if you will get the same result. Well, other than that, that's it for today. Thank you very much and good luck.