Reformed Disk
Calculus
Level
3
A unit disk (radius = 1) is partitioned into an inner circular region of radius \((r < 1)\) and an outer region consisting of the area between concentric circles of radii \(r\) and 1 respectively.
The inner region is preserved, and the outer region is reformed into a circular disk with equivalent area. Thus, the combined area of the two resulting disks is equal to the area of the original unit disk.
Which value of \(r\) (to 3 decimal places) maximizes the sum of the circumferences of the two final disks?
Note: Image might not be necessarily be up to scale.
by
Steven Chase