2 Math Questions

Test Preparation SAT Preparation
1

<p>Please help me out with the following questions:</p>

<ol>
<li><p>A cube with a volume of 8 is inside a sphere. What is the diameter of the sphere?</p></li>
<li><p>Picture of the question: [url=<a href="http://cl.ly/JeOx%5DIMG_1096.jpg%5B/url"&gt;http://cl.ly/JeOx]IMG_1096.jpg[/url&lt;/a&gt;]&lt;/p&gt;&lt;/li>
</ol>

<p>Help would be appreciated. Thanks.</p>

2

<p>Could you give the answers to both? I’m pretty sure I know how to do them, but I don’t want to somehow give you the wrong answers.</p>

3

<p>(1) This question isn’t worded very well - I’m guessing that they mean the cube is inscribed in the sphere - otherwise there is not a unique solution. In this case we are looking for the “long diagonal” of the cube. First note that the length of a side of the cube is 2 (becasue 2^3=8). We can now use the generalized pythagorean theorem: d^2 = a^2 + b^2 + c^2 = 2^2 + 2^2 + 2^2 = 12. So d = sqrt(12). Since this is a grid in question just type sqrt(12) in your calculator and copy the first four symbols: 3.46.</p>

4

<p>(2) x inversely proportional to y means that the product xy is a constant. For easier readability let’s just make the constant 1. So xy=1. Now solve for 1/x^2:</p>

<p>y=1/x
y^2 = 1/x^2. </p>

<p>So we see that 1/x^2 is a constant times y^2 (the constant is 1). So y^2 is directly proportional to 1/x^2, choice ( E).</p>

5

<p>Muffinman Already got the answer, but thanks. </p>

<p>DrSteve, really appreciate it! Yeah I paraphrased that first question, the answer is indeed 3.46. Alright, thats how I did it and wanted to make sure I did it right :)</p>