The ratio has a lot to do with storage.
Tape wrapped around a hub. Tape is thin, but not completely, so wrapping hundreds of meters on tape results in a change in diameter of the spool. This impacts the rotational velocity needed to get the linear meters-per-second on the tape media consistent as the diameter changes when you wind down from a full spindle toward the hub. IBM has variable speed motors and other clever technologies to handle this adjustment.
Disks spin at consistent speeds, but tracks on the outside edge travel faster across the head than the inside tracks.Currently, the top speeds for disk are 15000 Revolutions per minute (RPM). As faster rotational speeds are investigated, the researchers find they need to make the diameters smaller to compensate.
The diameters of disks were based on "U", the unit height of standard 19" racks. A "U" is 1.75 inches, and standard floppy diskettes were 5.25 inch (3U) and 3.5 inch (2U). For those who have a difficult time remember how many inches a "U" is, it is the height of a standard two-by-four (2x4) piece of lumber.
The value of "pi" has been calculated to over a billion significant digits. Here is a cuteapplet to use if you ever need the value to any level of accuracy.