- #1
bodensee9
- 178
- 0
Homework Statement
Hello:
This is a max/min problem. I am asked to find the rectangular box of maximum volume inscribed in a hemisphere of radius R.
Homework Equations
So I am wondering if I have set up this correctly. If say my length is x, width is y, and height is z. So, I would have max(xyz). And then would I have [tex]R^{2}-\frac{x^{2}}{4}-\frac{y^{2}}{4} = z^{2}[/tex] I am not sure if this is the correct relationship. And then my function would be: f(x, y) = [tex]xy(r^{2}-\frac{x^{2}}{4}-\frac{y^{2}}{4})[/tex]
I think I can maximize xyz using xyz^2.
thanks!