perplexus.info :: Geometry : Lotta Yotta

Lotta Yotta (Posted on 2002-10-13)

Business Week states that, "In ten years, the volume of online data accessible either on the Internet or on corporate networks is expected to approach a yottabyte..."

Currently, the largest named measure of data is the yottabyte (YB), which is exponentially greater than the zettabyte, exabyte, petabyte, terabyte, and so on. The yottabyte is approximately equal to 5X * 10^6, where X is equal to all printed matter that exists on our planet. More definitively, 1 YB=2^80 Bytes.

The highest-density digital tape (which is the highest-density medium currently in common use) made by one of the world's leading manufacturers stores data at a density of 124,000 bpi (bits-per-inch). Assume zero overhead for error-correction and -detection.

At a tape thickness of 8.9 microns, what must the diameter of a roll of tape be in order to store one YB of data, assuming that it is wrapped around a spool with a diameter of 0.5 inches and assuming that there is no space between the layers of tape?

Submitted by jusgre

Rating: 3.0000 (6 votes)

Solution: (Hide)

To find the diameter of the roll of tape:
I. Find the length of the tape:

A. Convert yottabytes to bits:
1 YB = 2^83 bits = 9671406556917033397649408 bits

B. Convert bits to inches:
9671406556917033397649408 bits/124000 bpi = 77995214168685753206.8500 inches

II. Using Step I, find the area of the "side" of the "piece" of tape.

A. Convert microns to inches:
8.9 microns/25400 microns-per-inch = .0003503937007874 inches

B. Length * Width:
77995214168685753206.8500 inches * .0003503937007874 inches = 27329031736271779.6669 square inches

III. Find the area of the end of the spool (a = π r²):

π * .25² = 0.1963495408493620 square inches

IV. Add the areas of steps II and III:

27329031736271779.6669 + 0.1963495408493620 = 27329031736271779.8633 square inches

V. Given IV, find the circle's diameter (2 * (√(A/π))):

√ (27329031736271779.8633 / π) = 186537942.3224 inches

VI. To make this number a bit more manageable, let's convert to miles:

186537942.3224 / 63360 inches-per-mile = 2944.0963 miles

This is roughly 37% of the diameter of the planet earth and almost one and one half times the diameter of our moon. Now that's a Lotta Yotta!
The entire equation can be expressed as:

(2 * (√((((2^83)/124000) * (8.9/25400)) + (π * ((0.5/2)²)) / π))) / 63360 = 2944.0963

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution	Antonio	2003-09-03 15:38:11
re(3): The hard part	levik	2002-10-15 02:11:37
re(2): The hard part	TomM	2002-10-14 22:45:50
The easy part	Ender	2002-10-14 06:54:24
re: The hard part	levik	2002-10-14 06:10:26
The hard part	TomM	2002-10-13 11:18:11

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