WEBVTT
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we're giving kind of challenging problems. Let's go ahead
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and walk this together. So we're told that a
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right circular cone has a base radius of one based
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radius of one and a height of three. Okay
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. Of cube is inscribed in the cones. About
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one face of the cube is contained in the base
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of the cone. What is the side length of
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that cube? Okay, well, we need to
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consider the cross section obtained by slicing vertically by a
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plane that contains diagonal off the base of the cube
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so we can obtain the rectangle of height. We'll
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just call that high s. So the height s
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side length of the cube and the with which in
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the note that as rad two times s rad two
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of us. Um and we could do this by
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using similar triangles. So we go ahead and we
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say, All right, so we have ah,
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height of three in a base of one, and
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that is equal to s all over. One minus
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1/2 off. And then we take it this bad
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boy equation right here, the, um the square
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root of two times s perfect. So now we
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can go ahead and say that as is equal to
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six over three, Red two plus two. If
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we go ahead and we simplify this or we're basically
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we're first going to expand this to get a light
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denominator so we can say six times three rod to
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minus two all over three Rad two plus two times
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three rat to minus two. That is equal to
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nine. Rad to minus six all over seven.
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And that is our answer. That is our answer
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. Who want to go ahead and we want to
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go ahead and now evaluate this. We can say
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this is approximately 0.9611