Baking the biggest pie

This week’s Riddler Classic is about baking the biggest pie. Just in time for π day!

You have a sheet of crust laid out in front of you. After baking, your pie crust will be a cylinder of uniform thickness (or rather, thinness) with delicious filling inside.

To maximize the volume of your pie, what fraction of your crust should you use to make the circular base (i.e., the bottom) of the pie?

Here is my solution:
[Show Solution]

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