Chapter 10.B, Problem 81E

Blu-ray Geometry. The capacity of a single-sided, dual-layer Blu-ray Disc is approximately 50 billion bytes. The inner and outer radii that define the storage region of a Blu-ray Disc are r = 2.5cm and R = 5.9cm, respectively.

1. What is the area of the storage region in cm²?
2. What is the density of the data on a Blu-ray Disc in millions of bytes/cm²?
A Blu-ray Disc consists of a single long track or “groove’ that spirals outward from the inner edge to the outer edge of the storage region. The width of each turn of the spiral (essentially the thickness of the groove) is d = 0.3 micrometers ( 1 micrometer = 10-6 meter). It can be shown that the length of the entire groove is approximately $L=\pi (R^2-r^2)/d$ . What is the length of the spiral track on a Blu-ray Disc in cm? in miles?