the-dimensions-of-a-rectangular-solid-are-sqrt5-inches-by-2sqrt3-inches-by-2-sqrt3-inches-express-th

Question

The dimensions of a rectangular solid are $\sqrt{5}$ inches by $(2+\sqrt{3})$ inches by $(2-\sqrt{3})$
inches. Express the volume of the solid in simplest form.

M S · Accepted Answer

So we have a rectangular solid so rexing of solid. It&#x27;s just a three by three by three right tingle. So it&#x27;s just three d. So we know that the dimensions are 35 but two plus three bye to minus 43. So the height here he&#x27;s also these two minus bearing three. They were looking for the volume. So the volume is length times with times heights and we have all three of these numbers. Sorely is Rupa our wit ISS two plus Route three on our highest to minus 43 Because multiplication is can you can switch the numbers around and still get the same result. I&#x27;m going to multiply the last two factors. First on women will supply this and this First some slim bring down the Route five And now Reynolds up are the first term. So two times he will give us for route three times to give us negative to room three, then the center terms here Now give us positive 23 in the last times here going to give us negative three because a radical religious cancel, we&#x27;re gonna simplify the inside. So you have four minors theory. Don&#x27;t give us one. And because these are the same radical here, we can combine your coefficient. But negative two was to give us zero. So these metal turned his counsel&#x27;s out. They were just left with one. So now we have skirted Bob Thomas one. It&#x27;s just wearing fuck. So the volume is swearing fug and inches square interest cube because it&#x27;s falling in turn.

Meredith Moody · Answer

All right. So I am finding a missing dimension here of a rectangular solid. So the first thing we&#x27;re gonna do is first in one day was switched my pen dollar, the real. The first thing I&#x27;m gonna dio after that is I&#x27;m gonna sketch my solid, so I have this. Oh, well, that really didn&#x27;t go. Well, let&#x27;s try one more. There we go, and we&#x27;ll try that one more time. Here we go. Whoa. That one. That one worked out really nicely, all right? And I know that it says the base is a square, and, um, the height has a five is five inches. So if the base is a square, that means the length and the width are equal, and then the height is five. But then it also tells me that the volume of my cue upside my rectangular solid is 125 cubic inches. I&#x27;m gonna make that five a little nicer. Well, now I can set up my my formula, which is a volume formula for a rectangular solid, is length. I was with times height, and I&#x27;m going to now put in a minute or identify the values that I have. I have the volume of said solid as 125 cubic inches and I have the height as five inches. And so now I&#x27;m going to substitute these into the equation. So I have 125 as the volume equals the length and the wit and the height. And I&#x27;m gonna solve this because oh, you know what it says The square is a bait of the basis of square. And so because the length and the width are equal, I&#x27;m going to simply write that this is a site. So because this is a square, I&#x27;m gonna write that this is a side and this is a side. So I&#x27;m gonna put this in. I&#x27;m actually gonna put this year so belated that the length equals the wits because the base is a square. McGuinness All right, so then I&#x27;m gonna have side times the side times five. So now I&#x27;m gonna solve. So I have 125 equals side times. Side is side square, times five and I&#x27;m gonna divide out my five and I&#x27;m gonna get 25 equals the side squared and I&#x27;m gonna take the square root of both sides because I have a exponents of squared and the square of s square is s on the square. 25 is five. So my side length for my base is five inches. And if you know your perfect cubes, you probably didn&#x27;t even have to do that much work. Because if you looked and it said that the base was a square and you saw the volume was 1 25 and the height was five. That means that it was a perfect cute. So you would have known that this five times five times five. But if you don&#x27;t know your perfect cubes, uh, then you would have had to work it out like this And just, you know, by the way, you should know your perfect cubes. And he stuck to five eso my side Lee is five inches.

James Kiss · Answer

We&#x27;re looking at this prism, and we want Teoh Ryan expression that would represent the volume of B region. Outside this, the smaller prism inside the volume of a prism is length, times with times height. So we would have in a times a times for a that would be of the whole thing. But then we need to subtract out the, um center, which is, ah, length of B A with the B in the height of four A. So that would be be times B times for it. We need to take out. So what do we got here for a cubed minus? For a e squared factor form of this, though, we can take out a four a and we&#x27;re left with a squared minus B squared and that can be broken down to a difference of squares for a times a plus B times a minus bi

James Kiss · Answer

when looking at your solid Here the volume is length, times, weight, times, height and for our overall, one would have a volume of a times a times three a. And then we will take out the center of it, which is be times B times three A. It comes with times higher. So we have three. A squared minus three a B squared in factored form. We could take a three a out or left with Okay minus b square. I made a little mistake. Here is that square. This is 38 of the third and so we can still take out just in a But that makes this in a square. And then we can factor Ace grade my speech bird further to be a plus B times a minus bi so 38 times April speed times a might.

Sarah Vo · Answer

Okay, so we&#x27;re going to be solving for a square period May. So you just want to write down your basic pyramid equation for volume, which is I&#x27;m sorry. B equals length, times width, times high over three. Simple. But now we&#x27;re gonna label down all the variables that we know. So we know that our length is five, You know that are with is also five. And we know that our height is six. So just plug it in. So we have V equals five times. Five times, 6/3. Another way you can write this equation is ve goes five square times six equals three. This wants more of a simplified one. Justo, make it a little easier. But either way you write your equation. It&#x27;s still going to come out as the same answer. So after that, we&#x27;re just gonna plug it. We&#x27;re just gonna solve everything. So five times five times six is equal to 150 over three. Volume is going to be 50. Make sure you do label and include your units in your answer. So it&#x27;s going to be cubic meters as and the power of three Q. So what? She was fairly easy. But if you have any questions or concerns, please feel for your reach out. Thank you.

Brandon Fox · Answer

The first step in the problem is to substitute the values of length with in height into the problem. So we&#x27;ll have volume equals 1/3 times, six times, five time seven. So when we multiply all these together, we&#x27;re gonna get 71 3rd one ABC throughout time. Six times five time seven 70 which is 70 feet cute.

Problem

The lengths of the legs of a right triangle in fe…

Problem 44 Hard Difficulty

The dimensions of a rectangular solid are $\sqrt{5}$ inches by $(2+\sqrt{3})$ inches by $(2-\sqrt{3})$
inches. Express the volume of the solid in simplest form.

Answer

$\sqrt{5} i n c h^{3}$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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$\sqrt{5} i n c h^{3}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry