<p>Hey guys, could you please explain this problem to me? My mind is going blank...</p>
<p>Point P is the center of one face of a cube and point Q is the center of the opposite face. If the length of the shortest possible path from P to Q along the outer surface of the cube is 2SQR2 centimeters, what is the volume of the cube, in cubic centimeters?</p>
<p>Thanks in advance.</p>
<p>Is the answer 2SQR2 for the volume as well? If so I’ll post my solution.</p>
<p>Yeah, the answer is 2SQR2. I would greatly appreciate a solution. :)</p>
<p>The shortest possible path is a straight line. It might be easiest to view it as if the cube were flattened out like you were looking for surface area. The distance from P to Q is 2SQR2. If you draw it out, you could tell that that is equal to twice of one side (P to the edge is half of a side. That edge to the other edge is one side length. That edge down to Q is half of a side. Ergo, added up, twice of one side). Divide that by two to get what one side is (SQR2). Cube that number for the volume.</p>
<p>…in other words, the answer is 2</p>
<p>The answer is 2SQR2 because SQR2 is one side and SQR2^3 is the volume…</p>
<p>Was this one the PSAT today?!</p>
<p>^ No, it wasn’t</p>