Quick Geometry problem needing explanation

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1

<p>I hate geometry :P</p>

<p>Well, here is the problem:</p>

<p>A Sphere is inscribed in a cube that has edges of length 8. What is the distance from the center of the sphere to a vertex of the cube?</p>

<p>Thanks.</p>

2

<p>it’s over 9000</p>

3

<p>I’m no math wiz, but this is how I would do it. I think it’s right.</p>

<p><a href=“http://i25.■■■■■■■.com/1zx2yrn.jpg[/url]”>http://i25.■■■■■■■.com/1zx2yrn.jpg&lt;/a&gt;&lt;/p&gt;

4

<p>my book says the answer is the square root of 48.</p>

5

<p>Is this a question from a SAT released by the College Board? Or is it from like Kaplan, Barrons…</p>

6

<p>Yes, the answer is the square root of 48. The diameter of the sphere is 8 since the sides of the cube are 8, so the radius is 4. In order to get from the center of the circle to a vertex, you need to travel a distance of 4 in each of the three dimensions. This distance is (4^2 + 4^2 + 4^2)^.5 or the square root of 48.</p>

7

<p>I really doubt that this is from the BB…</p>

8

<p>i have a really simple method of figuring it out. the length of the diagonal of a cube is always the square root of 3 times the side length. So 8<em>(squareroot 3) is the diagonal. Because you want to go to the center of the cube aka the center of the sphere, you multiply the diagonal by 1/2 so you get 8</em>(squareroot 3)/2. </p>

<p>and btw thats equal to the squareroot of 48.</p>