Evaluating an algebraic expression in a word problem | Algebra I | Khan Academy

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“The surface of a cube is equal to the sum “The surface of a cube with side length x” – from the faces of its six walls. ” Let’s illustrate this. I like to present things visually. If this is the cube, we can see 3 of its walls. 3 of its walls face us. But if it was transparent, we see that the cube actually has 6 walls. 1, 2, 3 front, then this one is below, this one is at the back and this one is also at the back. You have 3 walls per cube. So I believe what they say. that is, if it is x, it is x, this is x … – “is given by the expression 6x ^ 2.” This is also logical. The area of \u200b\u200beach side will be x by x, which is x ^ 2, and we have 6 walls. So this is going to be 6x ^ 2. “Jolin has 2 vessels in the shape of a cube, who wants to paint. One cube has a side length of 2. ” This is a cube here. I will try to draw it as best I can. This here has a side length of 2, these are its dimensions. “The other cube has a side length of 1.5.” The other cube will be slightly smaller. It has a side length of 1.5. That’s 1.5 by 1.5 by 1.5. “What\’s the total surface she needs to paint?” We know that the surface of each cube will be 6x ^ 2, where x will be the length of the side of this cube. That is, the surface of this cube is here will be 6 … Let me do this in the color of this cube – this will be 6 by x where x is the length of the side of the cube. The cube has equal side lengths, that is, length, width and height – they are all equal. For this cube the surface will be 6 times (2 squared). Then, the surface of this cube will be 6 times (1.5 squared). If we want the total surface it needs to paint, this will be the sum of the two cubes. So we’re just going to put these things together. If we want to calculate the first here, this will be 6 by 4. This is 24. And this is here it will be a little more complicated. Let’s see. 15 by 15 is 225. That is 1.5 by 1.5 is 2.25. 1.5 squared is 2.25. And 2.25 by 6 – let me multiply that. 2.25 to 6. Let’s see. We will get that 6 by 5 is 30. 6 over 2 is 12, plus 3 is 15. 6 over 2 is 12, plus 1 is 13. I have 2 digits after the decimal point – 13.5. That will be 13.5. And if I add these two, that will be equal to the total area, which she has to paint, which will be equal to 37.5 square – I guess they didn’t give us the units. 37.5 will be this total area of \u200b\u200bsquare units, whatever these square units are.

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