<p>A sphere of radius r inside a cube touches each one of the six sides of the cube. What is the volume of the cube in terms of r?</p>
<p>a)r^3
b)2r^3
c)4r^3
d)4/3(pie)r^3
e)8r^3</p>
<p>B, and this is not hard at all.</p>
<p>Just think about it. The diameter of the sphere would be 2r. The diameter would be the length of one of the sides. In a cube, the volume is (edge)^3. In this case the edge is 2r, so the answer is 2r^3.</p>
<p>Actually it would be e… because it’s (2r)^3 not 2r^3.</p>
<p>Oh wow; that wasn’t bad at all. And I just checked. It’s E.</p>
<p>Oh right, it is!</p>
<p>It is still easy, just a little tricky.</p>
<p>I WOULD NOT HAVE GOTTEN THAT WRONG IF I HAD SEEN IT ON PAPER, FOR EXPONENTS ARE A LITTLE TRICKY WHEN TYPING</p>
<p>You don’t really have to defend yourself with caps… lol</p>
<p>haha just wondering: why did you ask us instead of looking in the book? not trying to be offensive or anything</p>
<p>If the sides of the sphere touch all the sides of the cube, then the radius of the sphere must be half the length of each side of the cube. The area of a cube is side^3, or side<em>side</em>side.</p>
<p>So if r = 1\2 of the side, then 2r must be the side lengths of the cube.</p>
<p>(2r)^3 = 8r^3, E</p>
<p>
</p>
<p>Don’t worry, it’s the SAT. It’s testing how well you can read fine print not your mathmatical skills. I got confused too between the 2 answers, partially because of how it’s written and just what the SAT likes to do.</p>
<p>sorry children its 8r^3…
did this question yesterday on a test…
got it right</p>
<p>but i mean like if he would have posted a picture of the question…</p>
<p>i would have gotten it right for sure.</p>
<p>^This kind of thinking gets you in trouble on the SAT… I’m not saying that you can’t do it, but misreading questions and the “oh, I’ll get it right next time” mentality will cost you serious points on test day. I know, because I was one of those people.</p>
<p>oh haha no offense taken. I was just double checking because I can’t check this answer until I finished the WHOLE test. :)</p>
<p>But I saw in in TYPING, not in actual written numbers.</p>
<p>I do NOT have that mentality.</p>
<p>I glanced at the answers and thought it was B… >.<</p>
<p>I have to remember to double check exponent problems now!</p>
<p>Egbert:</p>
<p>I’m not trying to offend you or anything. I’m just pointing out something that I think you should take note of. If you don’t want to take my advice or if you feel like you don’t need it, that’s perfectly fine.</p>
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</p>
<p>That’s why a smart fellow created the ACT. You aren’t tested on noticing unimportant details. Instead, you’re actually tested on mathmatical abilities.</p>
<p>I also tend to make a lot of stupid mistakes on the SAT math and I really don’t care because I know it doesn’t mean anything. The only time I get myself into a hassle is when I can’t solve the question, and that is fairly rare. The mathmatical skill difference between someone who is good at the SAT math and someone who is not is very subtle. Just another of my SAT rants. :)</p>
<p>E - come on now… :)</p>
<p>yeah, the ACT does not try to trick you quite as much, but the test is very paced very quickly. One is a power test, one is a speed test. You may be better at one than the other, it depends on the individual.</p>