Technically correct, but I think it can be assumed from the question that it's referring specifically to a conical frustum. Of course, the answer is then that t

Technically correct, but I think it can be assumed from the question that it's referring specifically to a conical frustum. Of course, the answer is then that the shape of such an object would be, well, a conical frustum, which renders the question tautological. I believe that the intent of the question is something like “What are the dimensions of a conical frustum having 1/2 the volume of a cylinder, with the same base and height?”, or, put another way, what would the ratio of the diameter of the top of such a frustum be to its base? The answer being somewhere between 0 (as it would be for a cone) and 1 (for the cylinder). I'm sure there's a formula to calculate this value for a given volume, but I don't really care to figure it out at the moment. Although, it might be interesting to see if such a formula scales to values for the relative volume above 1, creating an “inverted” conical frustum…