Correct Puzzler answer Jan22 2011

It is assumed that the object being balanced and the fuel are both Homogenous… which they are.

There are already two other threads about this. It doesn’t matter if they are homogenous; the center of gravity answer is still incorrect.

it1979 is right. The center of gravity is close but incorrect. The volume of the half cylinder needs to be halved. This corresponds to halving the area of the semicircle, and a line through the centroid doesn’t do that. Area moments are balanced about the centroid, not areas. The attached file shows the equal-area calculation for a 20-inch diameter circle, where the equal-area line is 4.04 inches below the diameter. The centroid is 4.24 inches below the diameter.

At least you are a bit more polite this time.

Sorry I missed the other threads, which already settled this issue.