This week the question is: Can You Make the Biggest Bread Bowl?
I have a large, hemispherical piece of bread with a radius of 1 foot. I make a bread bowl by boring out a cylindrical hole with radius r, centered at the top of the hemisphere and extending all the way to the flat bottom crust.
What should the radius of my borehole be to maximize the volume of soup my bread bowl can hold?
And for extra credit:
Instead of a hemisphere, now suppose my bread is a sphere with a radius of 1 foot.
Again, I make a bowl by boring out a cylindrical shape with radius r, extending all the way to (but not through) the curved bottom crust of the bread. The central axis of the hole must pass through the center of the sphere.
What should the radius of my borehole be to maximize the volume of soup my bread bowl can hold?
Highlight to reveal (possibly incorrect) solution:
Calculations. WolframAlpha assistance.
In my calculations I create a formula for the volume of the cylinder, depending on r. I then find the maximum volume. At r = √(2/3) foot, approximately 0.817, the volume is 2π/3√3, approximately 1.209 foot3.
And for extra credit:
ETA: I interpret “a cylindrical shape” as being the same as a cylinder. Flat top, flat bottom. Others interpret it differently.
Everything is multiplied by 2. The radius ends up being the same.
Stuff from ommadawn.dk (Lise Andreasen) 
