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While making jar; potter removes part of clay sphere and stores the clay from the removed Part box with dimensions feet; feet, and feet: She uses the expression bel...

Question

While making jar; potter removes part of clay sphere and stores the clay from the removed Part box with dimensions feet; feet, and feet: She uses the expression below to calculate the number of jars she can make In the same manner before the box Is full_ According to this expression_ what Is the volume of each part of the clay sphere the potter removes?numort Jars thot con bc Walde IDonc tc storage box192XYZnamnnynacunuuicublc feetcubic feetcublc feet192cubic feet

While making jar; potter removes part of clay sphere and stores the clay from the removed Part box with dimensions feet; feet, and feet: She uses the expression below to calculate the number of jars she can make In the same manner before the box Is full_ According to this expression_ what Is the volume of each part of the clay sphere the potter removes? numort Jars thot con bc Walde IDonc tc storage box 192XYZ namnnyn acunuui cublc feet cubic feet cublc feet 192cubic feet



Answers

What is the formula for the surface area of a box? Therese designs and builds metal sculptures. One particular sculpture is to be a large cube that will rest on one of its corners. She will cover the cube with panels that are 1 square foot in size. If the cube is to be 16 feet on each side, how many panels will she need to cover the cube?

Interior radius. Measurements of pottery shard coming from a pot with a flat button and circular cross sections were made every four centimeter from the bottom of the pot to the top. Using Simpson's rule, we want to estimate interior volume of the but to the nearest 10th of a leader, we went knowing that one leader equals 1007 mirror. Cute. So if we is look at the craft given. Yeah, we can see that the baht is more or less like this, uh, picture here. But of course, as Thiebaud come from er on archaeological bead, We have, uh, the but not in integrity. So there are some parts that are lost during the geological time, but the measurements of the radios correspond to different heights. The vertical axis are given on the graph, and we are We have written them here on this table. So for height zero, we have a radius of 18.5 centimeters. Yeah, For four centimeters of height, we have 11.5 centimeters as's radius or height of eight. We have 13.8 centimeters of radius, 12 centimeters of ICT. We have 15.4 centimeters of radius and off resisting 16 centimeters. Hide. We have 16.8 a centimeters of radius. So these are the measurements made every four centimeters going on the positive direction off the Y axis. So the cross sections off thes part made are obtained by intersecting the interior volume of the bob with horizontal planes parlor to the bottom of the but our circles with radios. That depends on the height. We are putting the plane so we can say that deep. Um, Okay. Interior volumes. Okay, we're going to ready here. Interior volume off the pot is through the integral from zero to the total height measure. That is 16. Yeah, off the areas of thes circles, that is, by times, radios square. And we're not this radios depend on the height. Why? So this is the expression that give us interior volume of the pot. So this is by times integral from 0 to 16 off our square off. Why differential? Why so we got to estimate for approximate is integral here. And for that, we're only is seem since rule what? And as we see in the graph, the values off heights are separated by four units that is every four centimeters. So we have that age, the value of age we had to use pain seems his rule is four and we have 123 47 tools. So we had to calculate as four, which is going to be the approximation to the integral from zero to 16 of our square of Why. So the function we are integrating here is the square of the radius. Okay, so as for is equal to age thirds, that is four thirds times the function evaluated at zero Eddie's R squared zero plus four times are square at four was two times are square at eight plus four are square at 12 plus our square at 16 and it is the approximation to the interval. So the interior volume off the part right approximately will to buy times thes approximation here. So it is by as four that is four by thirds. Times are off zero square. There is 8.5 square plus four times are at four square trees, 13 0.8 square. Sorry, 11.5 here. So it's four times 11.5 square. Okay, those two times 13 0.8 square plus last four times 15 0.4 square plus 16 0.8 square. And so, uh, we got to use a calculator, and we find that this approximately equal to 9.2 69 eight times 10 to the 3rd, 3rd Centimeter Cube. And as we saw here, up one leader equal 1000 centimeters. Cure Cube, that is 10 to the third sitting here. Cute. So as we obtain here, they into the third city. Minuscule. We know that all these expression here iss one leader. So we obtained finally 9.2698 leaders. But we got to round the answer to the nearest 10th leader. So the actual answer is 9.3. Because the 3rd 2nd decimal we get to, uh, get rid off is greater than five. So can say that the interior volume. Yeah, off the But he's about 9.3. Leaders

We're working with a greeting shape. Let's start with this. Three D shape were only given one measurement off four. Well, when you're only giving one measurement that's saying that this is Ah, Cube or these are squares. That means they're all gonna have the same measurement all the way around. So I have four months late within height, so I have four all the way around. I want to find the volume for this kid. The volume equals Linz. Thomas Witt, Tom Side. Well, since I have four to make something have four for all three. So volume equals four Tom's four times four. Well, four times for 16 16 times 4 64 So volume equals 64. Now let's throw a unit of measurement in there. Let's say we're working with inches, so volume is gonna be 64 inches. And because we have a three D shape, that means we're gonna have cube, so value will be 64 inches. Q. That is what you do when you only when you given only one number

That's how were given a Que and this Cube would only give the one measurement. Well, it was a Cuban means is saying that all of these faces are squares. So of all the Pacers of squares, that means all of the measurements around are the same. Everything is 10 and all lines of 10. What's on the volume of this cute? So volume equals Let's Comes With Tom Site, the final given only one number. That means that one number represents all three. So volume it was. 10. Tom's Tune Times 10. Well, 10 times, 10 times 10 means the volume is 1000. Now let's add a unit of measurement. That's who were working with inches. Well, if I have interest, I have 1000 inches. Says this is a three D shape. That means I'm gonna have 1000 inches que This is our volume

Were given a cube. We want to figure out the base. Are the volume of this cube We have a cube? Yes. You just one side of So my side is 10. So this is simply saying that this cube is a square and all sides are equal. When will you give the one number your volume toe unequal. That side huge. So this is our side is tan. So that volume equals 10 cute or 10 times 10. I was 10. So volume was going to equal 1000. Now, let's And we actually had a measurement. Let's say we had inches. So I will put my unit of measurement inches. And because I work with three D shape, it would be cute. 1000 inches huge. So this is our volume. We're working with a que


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