Maximum area of a frustum bounded by the parabola y = -x² + 16 and the line y = 0

[mathwiz123]

Find the maximum area of a frustrum bounded by a paroloid and line y=0. (constraining parabola =-x^2 + 16.)

 

[grant9076]

Is it 4*64/3? (Quick mental calculation).

 

[mathwiz123]

Can you show how you did it? Cause this is something I've thought about after my son showed me his math homework a few years back. Found this forum, and decided to see if you guys knew.

 

[chroot]

Sorry, we don't provide the solutions to homework problems here. If you show your work and explain your reasoning, we can help you when you get stuck. BTW, the "my son showed me this a few years back and I can't stop thinking about it" line is unnecessary -- you aren't going to trick us into doing your homework for you.

- Warren

 

[mathwiz123]

I was actually serious...I understand that you find a lot of kids on the site. I thought of this problem today when trying to build a brace for a parabaloid shaped piece. I thought of a lot of different shapes to put in it. Cylinder, cone, etc. Frustrum came to mind and I thought of the homework problem. I'm sure I could consult any calculus textbook, but you folks seemed to provide interesting responses. If you want my "work" I know the ratio of radius and height of the "small" and "big" cone are equal. But that's all I know.