Intetertsploepaint(2,0,3)(-1,3,0)(2,-1,2)(-2,1,3)...

(1) 212 (2) 532 (3) 244 (4) 733

So this is one of those questions that you think you're done and then you have to remember you're not really done on. So I see this kind of error a lot with these kinds of questions, you really need to make sure that you are keeping track of your work so that you don't end a problem to suit. So here we are, given the information about how much area, uh, one can of paint can cover, which is 300 square feet. And because we have the word cover and we have square feet, that means we're looking at surface area eso. What I have is I have, ah, illustrated that he cylinder that is going to be covered in paint, and I've written down for set to the surface area of a cylinder formula that I'm gonna need to use now I need to get the values for the variables in my formula. Thankfully, I was given the radius and not the diameter, because if you get the diameter, of course you have to convert it to the radius or use it to get the radius. But because we got the radius Aiken just right that it's 12 feet on, then we also are given information that the height of the cylinder is 30 feet. Now, I can simply substitute those values into the equation into that formula for the surface area. So the radius is 12 everywhere I see in our but a 12 and the highest 30. So where this h is, I'm gonna have a 30. Now I'm gonna solve for my surface area. So I'm gonna rewrite my equation here, and I'm just gonna follow order of operations. So 12 squared is 144 exponents first. Then we have multiplication from left to right now. I'm not gonna approximate pie yet. I'm gonna leave it like this until the very end. And so I'm gonna rewrite this with the community of property. And that means I'm gonna dio two times 12 is 24. Sure, Vairo equals and 24 times 30 is 720. Now, I can factor out that pie and make this a look at the distributive property because it is. And then I can add my parentheses together and I get for 68 And so I have 864 pi square feet and Now I can approximate pie and a consummate pious 3.14 You can approximate pie by using the pi key feature on your calculator, but it's I don't think it's gonna change how many cans of paint we need to buy. So I'm just gonna use the approximation here, and that's going to get me. 2712.96 square feet is the surface area, Um, and just for you know, argument's sake. Let's say I did the other way. See, that's going to really change anything. Um, I get 2714. Okay, so you know off by about 1.5 square feet. So that's not that's not a huge deal. So now this is where you, a lot of people would normally say, Oh, cool, I'm done. But you're not done. Because if you really look at the question with the questions asking that question is asking how many cans of paint need to be purchased. Eso. Now we have to take the surface area of the cylinder, and we have to divide it by the surface area that one paint can can cover. So the number of cans is going to be related to the surface area of the cylinder divided by the surface area. The can can cover. All right, So the number of cans I'm gonna find out by using the surface area of the cylinder, which is 27 12.96 on. Then I'm gonna divide that by how much of this area each can can cover, which is 300 square feet. So when I do that, get nine and change. I hope someone on. Here we go No for three to, uh and, you know, just for argument's sake, if I had done, um, the other one, because I just I wouldn't be just extra sure that I'm not, you know, making too many rounding errors here. Yes, the other one turns into a 9.477 So it's about 100 of a difference. Eso what happens here is nine cans of paint isn't going to cut it, and nine cans of paint isn't going to cut it. We need more than nine because I can't buy, you know, four hundreds of a can. I can't do that. So I have to buy 10 cans because I can't buy part of a can of paint, so I'm gonna need 10 cans of paint to cover this cylinder, so I'm gonna have a lot left over, but that's how many cans I need.

So in this question, we're told that a can of paint ways £2.4 ounces and were asked how much six cans will wait. Three. Multiply this by six, and we basically get £12 and 24 ounces when we multiply. Each element by six and 24 ounces, we know is basically 16 ounces plus. Hey, don't see us, and 16 ounces is £1. So we get £12 plus £1.8 ounces, which gives us potato off £13 and it parents is, and that's the week.

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