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Actlvlty: How many cans of paint do you need to buy fto paint a closed water-storage tank in the form of an upside-down cone with the diameter of the base (at the t...

Question

Actlvlty: How many cans of paint do you need to buy fto paint a closed water-storage tank in the form of an upside-down cone with the diameter of the base (at the top) 1.2 m and the length of the sloping side of 1 m? One liter of paint covers 1.45 m? of surface and you have to buy the paint in 1-liter cans_cans are needed_

Actlvlty: How many cans of paint do you need to buy fto paint a closed water-storage tank in the form of an upside-down cone with the diameter of the base (at the top) 1.2 m and the length of the sloping side of 1 m? One liter of paint covers 1.45 m? of surface and you have to buy the paint in 1-liter cans_ cans are needed_



Answers

A can of paint will cover $300 \mathrm{ft}^{2}$. How many cans of paint should be purchased in order to paint a cylinder that has a height of $30 \mathrm{ft}$ and a radius of $12 \mathrm{ft} ?$

Using the picture and the dimensions of the observatory. Let's first calculate the surface area of the observatory, which would be equal to the surface area of the cylinder, plus the surface area of the hemisphere on top. So calculate surface area of the cylinder, two pi R H and the service area. The hemisphere is two pi r squared, and we're told that the radius is 14 ft, so to pie 14 ft. When the height is 30 ft plus two pi or squared and calculating the surface area of the observatory, you find that it's equal to 3872 feet squared. And then in the second half of the question, how many gallons air needed to paint the surface if it requires two coats? So we're told that paint is, um, one gallon of paint is 300 ft squared, so one gallon eyes equal to 300 ft squared. I'm 3000 years, 72 feet squared, and this is equal to 12.91 gallons for one coat, so we're gonna multiply that by two on. This would give us 25.81 gallons needed for two coats, so theoretically. Uh, since you cannot buy 20.81 of a gallon, we would need 26 gallons for two coats of paint on the observatory.

So for this question, we know that there's a room that is four feet my 14 feet and you need to paint it. And so you know, as a for high ceilings, so we can think of it like a bit of a rectangle. So we have eight foot ceilings. It was a 12 foot 14 foot, and so we need no, we need to create the walls, not the ceiling or the floor. So we know the area. Is he called to shoe times 12 times eight. Because there two sides evolved that dimensions of 12. We have cost two times 14 on his beat, which will get US 182 plus 224 which is equal your 416 feet squared. But we know that we need to print this twice because it needs two coats. You take 416 and loves port number two. She gets a after 32 feet squared. You know, we asked Honey, cancel pain are needed, so we know that one can. A paint can cover 600 scarf eat. So we take 100 32 Nevada by 600. She get us approximately one point 3867 so we know that we two cans of paint two paints the room

Okay, because we know that three camps are need to paint the floor of the cancer. Tried to paint the ceiling. Must be wary of ceiling over area of the four times the can required for the floor stuff. In other words, mathematically, this would be two pi r squared over pi r squared. In other words, it's just the formulas for the different shapes. Right ceiling divide by floor, times cans required results in six cans on. The reason why is because all of this stuff over here cancels was just two times.

Hi, everyone. So today we're going to learn more about the volume off solids. So given this question, we have a si lo Asi Lo is basically a cylindrical body with ah hemispherical dome on the top. Just to give you an idea. This is usually used like the store arise O r. Such kind off, huge amount of rise are that kind of dry products aimed. So it's a cylindrical body and its hollow only inside and it has a hemispherical door to top off. So the question Let's see what's what other things that's given the question. So we have been given with the high cough. Be cylindrical part off the sea look, and that would be 20 meters. We also have been given with B guy meter off the seal, the wit off the seals so that with ease by a meter theme, the Sea Rover beaks 10 meters. So I'm going to denote that as each as a hike and be as the diameter. So if the diameters 10 the know that the radiant is going to be de divided by two and there would be 10 divided by two, and that is a five meter So one thing that always check in all of these questions is that all the units match in this question. We don't have to worry about it because all of them are given meters. If not, that would be a first step to convert all of them to the scene unit. Now, going back to the question, it sees that it takes about two cans of paint to cover the dome. The hammer stoical door. You can paint the hemispherical dome using two counts, two cans off paint. So what we have to find is how many cans off? Pained? Would it take us the cover? Be rest off B C. Low exterior. So what is the rest off the sealer exterior? It would be be soon to go part right? So how much pain would take us to cover the cylindrical part of this seal? So let's see. Let X be be number cans required. Took things. The cylindrical part of Cee Lo. Okay, so let's denote eight with a different color so that you know, we know what's. It's more easy for us to start out. So this is the part the exterior of the Cee Lo. There has to be painted using X number of cans Can, Uh Okay. Okay. So what? All hot have we been given? But we have been given. But the height of the cylinder we have been given with the diameter of the Cee Lo and the radius of the Ciro. So, no, we know that it took two cans of paint to cover the outside off the hemisphere. And that would mean the volume, right? The volume off the hemisphere. So let's find out. What's the volume off the hemisphere? So what is the formula for? Ah, spear. That's eso. What is what is it happened to be on him? Experience An exact half of Shakespeare, right? So what is the volume off spear like Started spear. Okay, what would that be That ISS for by three. Hi. In two. Let me use hers, Planks. Fulbright three by our que bright. Okay, Okay. So if that's the walling off a spear, what would be the volume of the hemisphere for living for hemisphere would be the exact half. Afraid right. So it would be one by two providers meaning to four by three Manger. Hi. I don't care. Are Rex the Lydia's mean, are you Are you are okay, so we know that. Okay, So what is the volume off the hemisphere given here? Let's let's find that qualifying that up. So that would be one light to into four, divided by three. So let me let me cancel about, and that would be cool. We got two divided by three. You do. Qari Inter 5 65 is the radius of this five. Not to buy with five 95. Now you can use a calculator and find out what's the what's the final answer for this. But I'm gonna wait on this, okay? I'm not gonna show you the final answer for this, cause I'm going to show you something of the end that's going to make a lot of few calculations. Easy. So we found out the volume off for hemisphere this particular hemisphere. Okay, the hemisphere shown here and now let's find out the wall. Him off the green, the shit part. That is the volume off the cylinders Now, what's the volume off a cylinder? The volume of a cylinder would be Hi. In care are square into HH eight easy hikes. So in this particular question. Where the what car is it gonna be? It's gonna be pi. And what's the value of pie? It's 3.14 to forget that. So pi into, ah, five into five into a church which would be training so again I'm not going to show you the final answer. I'm going to show you an easier way to solve these. So no, uh, in the beginning, off the question I mentioned about how the wall him off the hemisphere. That is the outside the exterior of the atmosphere. It's what's Waas painted, right? So how maney Kant's it took to paying the outside. That's the volume off this hemisphere. It took us, you walling. Oh, the atmosphere. It took us to cancer thing, right? Two cans of paint to cover the volume of the atmosphere. Okay, and now we need to find how many cans would have take to cover the exterior. What's the rest? The rest off the seal. And that will be what What's the wretched? The ceiling that speak cylindrical aren't fit. So we need to know how many cancer Spain is required for. That, and that is what we do know wanted us X on the top. Remember, X is the number of cans required to pain the cylindrical part to seal. So equating this we know Fine, X, what do you do? You cross multiply teas, right? You cross, multiply those and let me show you hear of the Exide. So X is going to be two cans of paint into two cans of pained into the volume off the cylinder that IHS Kai in two five Squire 5.25 I mean, Trenny. So I am having trouble writing with this. I hope it's all clear for you guys. Ah, to into a volume off the cylinder divided by the wall Him off the hemisphere. What is the volume of the hemisphere to buy three into pie into Five Cube being too. Oh, that's a no inter. Okay, I'm good at Racists. Okay, so we have this formula. See, this is the reason why I didn't, um, simplify these answers. Still final answer, Because in the end, you can just cancel out things, and that would make it so much more easier than using having to use a calculator or and if you're not allowed to use a calculator, you would just waste time, you know, multiplying all of this. So now our job is really easy, right? We just need to cancel out things. So those three is going to go on the top? OK, gonna rub it off from here? Children ings and three is gonna go. Just gonna right over the writings. The three is going to go over here. And what can we cancel? We can cancel too to we can cancel the five Squire and five square, which remains us. That's five. And you can castle pie pie. See how easy this is now? And five and 20. That would give us four. And we're left with four in the three. And that would be 12. So x is equal to that's right over here. X is equal to 12 Kant's. So this is a final enter. So this saves ecological clo cans. What does that mean? That's mean exact. It takes 12 cans of paint to cover the rest off the seal. The rest of the sealer would be the cylindrical part of the zero. And this is your final answer


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