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10 points REVIEW: You volunteered to hand out water; in cone shaped cups,at a marathon: Find the volume of water thatcan fill the cup to the top? Use pi and round t...

Question

10 points REVIEW: You volunteered to hand out water; in cone shaped cups,at a marathon: Find the volume of water thatcan fill the cup to the top? Use pi and round to the nearest hundredth:9.3 cmtype your answer_cubic centimetersPrevious

10 points REVIEW: You volunteered to hand out water; in cone shaped cups,at a marathon: Find the volume of water thatcan fill the cup to the top? Use pi and round to the nearest hundredth: 9.3 cm type your answer_ cubic centimeters Previous



Answers

Cone-shaped paper cups are used at the water cooler in many exercise facilities. Using the formula for the volume of a cone, the volume in cubic centimeters $(\mathrm{cc})$ of this cup is $V=\frac{\pi(3.8)^{2} \cdot 8}{3}$. Approximate the volume to the nearest cubic centimeter.

Hi, Merlakia. Question 27 which they ask us to find the volume of a cone, which is 1/3 pi r squared H is the formula that we're gonna be using. And the tricky part with these questions is they often don't give us in the question, the information that we actually need. We have to figure it out. And that's the case with this question. The diameter they tell us is 24 and we really need the radius. That one's easy, cause it's just half, so that's 12. But they also give us the slant height. And so we sometimes use the curse of eld to represent slant height. That would be 13. We need the actual height, but they give us information to be able to figure that out. So if we do a quick little sketch here, we can see that when we have a cone are slant. Height would be along the outside of the shape we need from the top, straight down to the middle of the shape, and then we actually have the radius, and this would be a right angle here, and we know that the radius from what we just calculated is 12 and we need this vertical height here. So since we have a right angle, we can actually use path a grand there, um, and say we have our height squared plus 12 squared. And it doesn't matter which way you write those because I'm your adding so and then equals the high pot news, which is our 13 squared. So age squared plus 1 44 equals 1 69 And if you know your pythagorean triples, you may already know the correct answer. And that's great. So H squared. When I subtract 1 44 from both sides, that's 25. So then age is gonna be plus or minus five, but a negative five doesn't make any sense here, so our height is five. So now we can go back to our formula because we have the information we need to be able to plug into it. And it's 1/3 pi r Radius remembers 12. We calculated that at the beginning, and then times are high, which is five now because they want to. In terms of pie, I'm just going to take the 1/3 time's the 12 square times the five and that gives me 240 and then I still need to multiply by pi because I haven't done anything with that yet. So we'll leave that there and then my unit's air, centimeters cubes and you're done.

Alright, We're working on Chapter 10, Section three um which is volumes of pyramids and cones. This is question number two and it's to find the volume of a cone with the given dimensions. The first thing we should talk about is our formula being volume is one third base um of the base area times the height. And so we have a cone here with um A radius of six cm and a height of seven. And so our base in this case is a circle. So we're going to go ahead and substitute um formulas into the formula itself. So volume In this cone is going to be equal to 1/3. Now the base area of a circle is found by taking pie times the radius squared and then we're going to multiply all of that by the height. So in the particular cone we have the radius is six, so we'll replace our with a six. So we have one third pie times six squared And then the height is seven, So Times seven. Okay We have 1/3 Times six squared is 36 to now we have 30. We have uh huh one third times six squared is 36. So 36 Hi times seven. Now the parentheses are there just to mark multiplication for us. So I can take 1/3 times 36 which is 12. So now I have 12 times pi times seven And 12 times seven is 84. And so we could say this is 84 pi centimetres cubed. Which would be the accurate answer if you were continuing to use this. We can also um run that through our calculator and get an estimate of Uh being approximately 200,000 jeez 263, 200 63 point eight nine centimeters cubed. And so we do have to answer options. Um the book did not specify whether to round or to leave in terms of pie, so we do have the option of 84 pi cm cubed or 263.89 cm cubed, and that should say approximately Okay.

This is Chapter 10, Section three Problem six. We are being asked to find the volume of a cylinder with the indicated cone removed. So we have a cylinder with a diameter of 12 and a height of 16. And we have a cone who matches those dimensions. So the first thing we're gonna look at is the difference between the two formulas. Volume of a cylinder is just the base area times the height of the cylinder. The volume of the cone is 1/3 of the base area times the height. This will help simplify some of our work here in just a minute. So the first thing we should do is we know that we need to take the volume the volume of the cylinder and subtract the volume of the cone. Okay, so the volume of the cylinder is base area times height. The base is a circle and the area of a circle is pi r squared. So we have pie they gave us the diameter, so the radius is six. So pi times six squared Times the height of 16. So six squared is 36. So we have 36 pie Times 16 and 36 times 16 Is 576 pie. So now we have the volume of the cylinder, the volume of the cone is one third of that. So we take one third Times 576 pi And 576 times 1 3rd or divided by three is 192 pi. So we're going to have Subtraction here and it's -100 one, 192 pi So 576 -192 is 300 84. And then of course we'll keep the pie on there and that is all in centimeters so centimeters cubed. And we can run this through our calculator and find that it is approximately 1000, 0.3 three seven centimetres cubed, so the volume of this cylinder with the cone removed is 384 pi centimeters cubed. Or 1000, 206.37 centimetres cubed. Yeah.

Hi with questions. Six. They want us to find the volume of a cone, and they want it both exact, which is in terms of pie and rounded to the nearest 10th. So the volume of a cone is 1/3 high R squared H. So we just need to plug in what they give us. So the volume is equal to 1/3. That part stays the same and high stays. And then we need to go look at her picture. Um, and they tell us that the radius is nine squared and then the height is 14. And those two I got from the diagram. So to find the answer in terms of pie, I'm going to actually ignore the pi symbol and just plug into my calculators, the numbers. So I'll take 1/3 times nine square times 14. And that's going to give me 378 and then because I didn't include the pie, I'll write it down here. And so it's 378 pi centimeters cute. So that's the exact answer. Or in terms of pie answer. And then we can just take that 3 78 times. Pi in the calculator. We get 1187 0.5 when you round to the nearest 10th centimeters cube for that one and you're done.


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