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*Precalculus Mathematics in a Nutshell*by George F. Simmons. Although the book is fairly small, many of the problems are quite challenging, at least for me.

I am stuck on this problem:

"The height of a cone is

*h*. A plane parallel to the base intersects the axis at a certain point. How far from the vertex must this point be if the plane divides the lateral area in two equal parts? If the plane divides the volume into two equal parts?"

I cannot provide much information on my attempt, as I do not really know where to begin with this one. The way I understand the problem so far, this plane basically runs through the cone horizontally and cuts it into a smaller cone at top and a frustrum at the bottom. The "certain point" is a point on the height plane that runs vertically and right through the middle of the cone, through the vertex. And the answer, I take it, must be written in relation to/terms of

*h*. (I often find that figuring out what the problem actually says takes much longer than doing the problem itself.)

Any help or hints would be greatly appreciated.