Recent content by booseek

I now see that the equation r/R=x/h is simply a way of deriving the ratio between the two triangles. I figured it out by drawing 2 equilateral triangles, one with each side equal to 3 and the other with each side equal to 9, plugging in the values for the variables, and getting a ratio as the...

Thank you for your detailed reply, HallsofIvy. I understand everything until this following point: r/R=x/h or r=(R/h)x. How does r divided by R equal x divided by h? Why are we dividing one side by the other?

I have taken a break from this problem and decided to come back to it tonight. Nearly two (!) hours later, I still do not understand how to derive the relationship between x and h. I wrote out the formulas (correctly this time) for the lateral area and the volumes of the big cone, the small...

Thanks for the replies. I tend to do my math in the evenings, so I will report back later tonight.

The attached image shows what I have so far. But as you can see, I do not know how to proceed from here. I'm assuming that I must write the answer in terms of h, but with so many variables, I'm not sure if I will ever reach an elegant expression. Should I set A1 and A2 equal to one...

Thank you for the reply. What I mean is that the "certain point" is where the horizontal plane (the plane parallel to the base) will intersect with the height plane (the line that runs from the vertex to the center of the circular base, creating a right triangle on both sides and dividing the...

I am working independently from the book 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...