<p>Given the volume of a cube is 8 cubic meters. Find the distance from any vertex to the center point inside the cube.</p>
<p>I thought I had done it correctly but I got this question wrong. How do you solve this?</p>
<p>If the volume of the cube is 8, then the side of the cube is the cubed root of 8, which is 2.</p>
<p>To reach the center, you need to draw a right triangle along the edge of the cube to the center; one side will be half the length of the side,
so a = 1
then, your straight line distance to the center from the edge will be half the diagonal of the cube - so it's 2 x sqrt(2) / 2 or 1 x sqrt(2)
b = 1 x sqrt(2)</p>
<p>Now apply the pythagorean theorem
1^2 + 1xsqrt2^2 = c^2</p>
<p>c^2 = 3
c = sqrt(3)</p>
<p>That should be the answer.</p>
<p>yes. i got sqrt(3) as well. </p>
<p>drawing a diagram is ALWAYS helpful for these kinda questions.</p>
<p>Any vertex? Wouldn't you have different answers with the different vertices?</p>
<p>The object is a cube, thus each vertex (where each plane intersects with another) is the same distance from the center of the figure.</p>
<p>Maybe I am bit slow at understanding math but I still don't get it. How is side b of the triangle equal to the square root of 2? Why do you multiply 2 by the square root of 2? I understand everything else but I don't know how to get the radical 2.</p>
<p>While this type of problem rarely appeared on the SAT and you could be solved via a couple of steps, it may be useful to add a couple of formulas to your arsenal. You never know when the ETS dudes will decide to "borrow" some material from the Level 2 Math. </p>
<p>For the diagonal length of a rectangular solid where l is the length, w is the width, and h is the height, the formula for the length of a diagonal is:</p>
<p>square root of (l^2 + h^2 + w^2)
or
square root of (length^2 + height^2 + width^2)</p>
<p>For the diagonal length of a cube, the formula is adapted from the formula for the diagonal length of a rectangular solid, with s = l = w = h. The formula is thus:</p>
<p>square root of (s^2 + s^2 + s^2) or sqrt (3s^2) or
s square root 3.</p>
<p>For the above problem, we need to define 1/2 of the diagonal, and the answer was simply 2/2 sqrt 3 or sqrt 3.</p>
<p>oh, now I get the question.....</p>
<p>I'm an idiot</p>
<p>Thanks Xiggi! I understand the problem now. It's actually been bothering me for days.</p>