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Case 3: Three dimensional objectthird dimension width W = 1.29 m at rest added to the rectangular object in case (length Lo 1.13 m, height H = 1.34 m) If this Thre...

Question

Case 3: Three dimensional objectthird dimension width W = 1.29 m at rest added to the rectangular object in case (length Lo 1.13 m, height H = 1.34 m) If this Three Dimensional object moves at a speed of v= 0.910 c relative to an observer; what is the object's VOLUME as measured by this observer? Keep decimal placesEnter 4 numibe'subm(5 attempts remaining)

Case 3: Three dimensional object third dimension width W = 1.29 m at rest added to the rectangular object in case (length Lo 1.13 m, height H = 1.34 m) If this Three Dimensional object moves at a speed of v= 0.910 c relative to an observer; what is the object's VOLUME as measured by this observer? Keep decimal places Enter 4 numibe' subm (5 attempts remaining)



Answers

An object is made of glass and has the shape of a cube 0.11 $\mathrm{m}$ on a
side, according to an observer at rest relative to it. However, an observer
moving at high speed parallel to one of the object's edges and knowing
that the object's mass is 3.2 $\mathrm{kg}$ determines its density to be 7800 $\mathrm{kg} / \mathrm{m}^{3}$
which is much greater than the density of glass. What is the moving
observer's speed (in units of $c )$ relative to the cube?

So we're given a three dimensional figure, but catches we aren't giving it in three dimensions were only given three views of it to dimension. Eso Let's try to reconstruct those Use it. We have one like this and it's leave of it. This length is 10. This length is 10 and this length is four. Uh, and we can fill in some blanks here. Miss Length is four. This total length must be 10. Um, so this we're left with here at six. Rate six plus four has to add up 10. So that's that's one view. The another view is from the top, we have something like this. Um, where this length they said was 10. Ah, this lengthen also is 10. Um and that's all that were given on this. But again, we can We can see that this and this thing that I just shaded in maybe I shouldn't use black shaded in this thing that all, uh, fill in with blue right here is this surface right here. So we can label this length six in this length or again and finally were given one more view from the side, which looks like do this and again we see that this this line right here is our lower level. Right? Uh, the thing that we're recovering in blue in the measurements that they give us this length is 10 which actually we already knew from are tough, you and that this length right here is for so that's good. Now we can use these three images. This is the front top, tough and side. We can use these three images to make a full picture of what this figure actually looks like. Eso I'm going to scroll down a little bit, but I still want toe heel to reference some of these. These images s so I know. And it looks rather rectangular. It's gonna look like this. This is images. This is 10 inches as well. Uh, excuse me. I think this is actually in centimeters, so these are, well, 10 units, whether it's inches or centimeters on, and I drawing my front kind of like this. Right? So I know that this is six. Excuse me? That's four in this. This length is six weeks. Um, and now I can also draw kind of the side here. Right? So got this view Our side view tells us that that length is 10. And at this length draw this side. This length right here is four. Cool. And now our top view fills in this. We already know that that length is 10 but we can get a fill it in like, um cool. So we have our composite figure, and now what we see is that this is a rectangular prison. We can think of it as a rectangular prism. That's just 10 by 10 by 10. Right, If I the draw that in green here this idea listen, pretend you're prison. This just 10 by 10 by 10. And then we cut out this piece That's four by four by 10. Draw that in blue, right? This piece is four by four by four. And it's kind of missing from our total rectangular prison. So let's let's go ahead and do that math are, um, all you is going to be the volume of the big rectangular prism, uh, minus the volume of the small rectangular prism. And I'm going to say our big rectangular prism is and by 10 by 10 and our small rectangular prison prism is four by four by 10. So the differences between these two should be The volume is left in our cellar here. So the volume of the big prison, Well, that's just 10 cube, right? 10 cubed. And then the, uh, volume of the small prison. Well, that's 16 times 10 160. Um, so what we're left with is 1000 uh, minus 160. Andi, that concept to be 108 140. And the units are centimeters cute. Um, so this is the final volume that we get for our composite image. Like this strategy was to just usar, um, different views of our solid, So construct kind of, ah three d idea of what this is and then break this down into, um, solids that we can easily find the value of and writing expression for the volume the total volume in terms of those easy, uh, solids that we could find the volume

So here we have different ways of looking at this object were given the front, the top and the side. So if I think about what this looks like, my front is this longer rectangle. My the top is a, um, triangle were thinking here about a, uh, triangular prism. And then that side will be this side over here. So that's our stuff. So we have a four centimeters here, seven centimeters and let's see, five centimeters. Oh, yes. The volume will be the base times, the height and our bases. This triangle which we're gonna need to take a closer look at because currently we don't have its height. We have the diagonal, we don't rotate. Luckily for us, it's nice sauce of this triangle. So if we drop this height down, we have bisect the angle and the offset side. Okay, so then we have a right triangle. Um, where this will not be, too. Because we bisected that side and we don't know the height X. So I'm gonna take a look over here that the x seven. That's for those two in the seventh. So using the pad, I'd like them. I can say x squared plus two squared equal. Sudden swear. So X squared plus four equals seven squared X squared plus four equals 49. So x squared will be to 45. Taking the square root of both sides That gets me X equals the square root of 45. Just leave it like that for now. Okay, So now if you go back to our volume formula So volume is the base times the heights, the area of the base will be 1/2 Is this triangle the base of the triangle? I must say this four times are hates its radical 45 and the height of the whole object, um, is going to be here for me. Five centimeters. So then the volume is going to be C four times five is 27 virtues 10 10 square root of 45 which, if I used a calculator to figure that out, that is going to be 67.8 to 67.1 cubic centimeters on that is answer. Okay,

So here we have different ways of looking at this object were given the front, the top and the side. So if I think about what this looks like, my front is this longer rectangle. My the top is a, um, triangle were thinking here about a, uh, triangular prism. And then that side will be this side over here. So that's our stuff. So we have a four centimeters here, seven centimeters and let's see, five centimeters. Oh, yes. The volume will be the base times, the height and our bases. This triangle which we're gonna need to take a closer look at because currently we don't have its height. We have the diagonal, we don't rotate. Luckily for us, it's nice sauce of this triangle. So if we drop this height down, we have bisect the angle and the offset side. Okay, so then we have a right triangle. Um, where this will not be, too. Because we bisected that side and we don't know the height X. So I'm gonna take a look over here that the x seven. That's for those two in the seventh. So using the pad, I'd like them. I can say x squared plus two squared equal. Sudden swear. So X squared plus four equals seven squared X squared plus four equals 49. So x squared will be to 45. Taking the square root of both sides That gets me X equals the square root of 45. Just leave it like that for now. Okay, So now if you go back to our volume formula So volume is the base times the heights, the area of the base will be 1/2 Is this triangle the base of the triangle? I must say this four times are hates its radical 45 and the height of the whole object, um, is going to be here for me. Five centimeters. So then the volume is going to be C four times five is 27 virtues 10 10 square root of 45 which, if I used a calculator to figure that out, that is going to be 67.8 to 67.1 cubic centimeters on that is answer. Okay,

Said. For problem number 33 we are given the volume of a three dimensional rectangular box and that is ill W h So I linked comes with times height and were also given all these dimensions. So our link this 10 our Witte IHS five and our height is three. So all we have to do is substantively is in. So that would be the equals 10 times, five times three. So that would be 10 times five is 50 50 times three is 150. Now, of course, this would be cubic units, but since we're not told what units this is and I'm just going to leave that as V equals 1 50 we're finished.


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