Applications of Calculus - Optimisation

Applications of Calculus - Optimisation
A group of go-cart enthusiasts want to build a track that is 500m long.
Show that by maximising the area of the track the track becomes a circle.
Understand one of the hardest and most common applications of derivatives, optimization and it's applications.
I hope it helps
Review the open topped box example to get a better grasp on applied optimization.

[@HaroldWalden]

Classic optimisation question, I hope it helps.