I am finding this one tricky.

Find the maximum volume of cube inscribed a right cone with radius 1, and height 3.

Why can't I do 3/1 = 3-x/x

If this was a cylinder, I'd have 3/1 = 3-h/r, and with a cube the sides are equal.

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- Jun 13th 2009, 06:24 PMGulhow to find maximum volume of cube inside cone
I am finding this one tricky.

Find the maximum volume of cube inscribed a right cone with radius 1, and height 3.

Why can't I do 3/1 = 3-x/x

If this was a cylinder, I'd have 3/1 = 3-h/r, and with a cube the sides are equal. - Jun 13th 2009, 07:06 PMmr fantastic
- Jun 13th 2009, 07:11 PMGul
why is it a 1/2 - x/2, and not just x/2?

- Jun 13th 2009, 07:15 PMmr fantastic
- Jun 13th 2009, 07:21 PMGul
They get this:

3-X / 3 = Xsqrt(2) /2 - Jun 13th 2009, 08:15 PMmr fantastic
Oboy. It's my day for dumb mistakes today. I have no tme now but I'll show where that comes from later.

Edit: The key is to note that when the cube is fit inside a cone, the longest side

is the diagonal of its top face. Read:

http://books.google.com.au/books?id=...esult&resnum=1

http://www.math.hawaii.edu/home/putnam/1998.pdf - Jun 13th 2009, 08:44 PMGul
Thanks!, just one question, why can you do the ratio I had before for a cylinder, but not for a cube

- Jun 13th 2009, 11:54 PMmr fantastic
- Jun 14th 2009, 12:07 AMGul
Thank you. Are there any other rules which are important for inscribed solids?