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Chapter 6

Test Yourself

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01:13

For any cube with edges of…

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So this one says. If the volume of the sphere is equal to the volume of a cube, what is the ratio of the edge of the cube to the radius atmosphere? So what we're looking for is the ratio of the edge of the cube of the radius of the sphere edge of the cube to the radius of this fear. So then that's the same thing as E as an edge of the cube to our radius of the sphere, which can also be written as e divided by our. So then it does tell us that the volume this fear is equal to the volume of a queue. So let's go in first to find the volume of a sphere and the volume of acute well. Cuba's easy because we know that it's basically a three dimensional square, and so it's made up of six squares, so normally, for any rectangular prison we would have length times, width, times, height. But because it's a square, we know that all the sides, all the length and the width and the heights are going to be the same. So then we can just call that e Cube because we can say each judge is a link for with or a height because they're all the same. So then, for this fear, we know that the equation is going to be for over three pi r cubed. And then again, since we know that they're equal, we're going to go ahead and set them equal to each other For over three pi r cubed is equal to e cute. So then, since this up here is what we're trying to mimic, we know that we want the e on the top, the numerator, and are on the bottom as Gemma Denominator. So we're going to go ahead and divide both sides by r cubed because then we're going to be its cancel out that our cute of the new writer and architect of the denominator and so we'd have four over three pi is equal to e cubed, divided by are cute. So then from here. So this is the tricky part. So in order to get rid of these two cubes, we want to take this whole side up here well, both sides. But we want to take this and razed it to the one third power. The reason we want to do that is because doing that is the same thing. I saying e cubed too. The one third power divided by our cube to the one third power. And we know that because of power rules, a number that a power that's raised to a power, it's like doing that power times that power. So we're just going to be multiplying these two things. So then three times, one third is just gonna be one, which is exactly what we want, because we want e to the first, which is the same thing as E. So then if we do that to both sides, we have four over three pi raised to the one third power is equal to e divided by our because that's the same dance, each the one divided by art, the one So then if we calculate this out, that's just going to become one point six one. So C is gonna be our answer here

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