<p>I think I found an error in "PWN the SAT". </p>
<p>On question 20 on p187, the question reads as follows:
--What is the volume of the largest rectangular solid that can be inscribed in a sphere of radius 4?</p>
<p>The largest volume is achieved when a cube is inscribed in a sphere.</p>
<p>The author of PWN the SAT states in the explanations that the diameter of the sphere is the same as the DIAGONAL on any given side of the cube. This, however, leads to the cube exceeding the boundaries of the sphere.</p>
<p>Now this site ( A</a> cube inscribed in a sphere - Math Central ) states that the diameter of the sphere is the same as the DIAMETER of the cube, not the DIAGONAL. This does not lead to any problems, and I'm pretty sure that this is the correct version.</p>
<p>Can you guys tell me if I'm right or wrong? This single question has been driving me crazy for at least the past hour.</p>
<p>FD is the diameter of the cube. In the link that I posted, the diameter is described as the distance from one corner to the opposite corner, so that accurately describes FD. </p>
<p>In the back of the book with the error, the diagonal is on one of the FACES, for instance FH is an example of a face diagonal. The author then bases the rest of the problem off of the idea that FH is the same as the sphere diameter. </p>
<p>Using the fact that FD is the same as the diameter, which is 8 in the problem above, how would I solve the problem?</p>
<p>D’oh, nevermind I was looking at one of the diagrams he (the author of PWN the SAT) drew incorrectly. I totally misinterpreted the whole explanation. </p>
![http://www.kjmaclean.com/Geometry/Tetrahedron_files/image028.jpg[/url]](http://www.kjmaclean.com/Geometry/Tetrahedron_files/image028.jpg%5B/url%5D){kind=link}
