Idea: Use current technology (DVD lasers, layering, and 1:2 lossless audio
compression formats) to:
 Create a half size (radius) "CD" with unknown (until calculated)
storage capacity based on that
DVDs are 4.6 GB
DVDs are of the same size as a CD.
Lossless audio compresses 1:2
 Create an unknown (until calculated) radius "CD" with 100 minutes
of audio based on the same.
 Figure out the capacity of each of these formats for:
A: 44.1 KHz/16 1:2 lossless compression
size = raw * 0.5
B: 66.2 KHz/24 1:2 lossless compression
size = raw * ( 66150*24 / 44100*16 ) * 0.5
size = raw * 1.125
C: 160 kbps lossy compression
size = raw * ( 160*1024 / 44100 *16 )
size = raw * 0.233
D: 16 kbps speech compression
size = raw * 0.0233

1: Half radius CD.
A fully fledged CD (i.e not "business card CDs" etc) has an inner radius of
7.5 mm and an outer radius of 60 mm. [1] The outer circle contains a small
area of nonrecordable material closest to the hole of inner radius as well
as at the very edge, and therefore has an effective recording area from 46/2
= 23mm to 117/2 = 58.5 mm [2].
Assuming we keep the hole, the recordable area of the old CD is
(pi*58.5^2)(pi*23^2) = 9084.805 mm^2.
Halving these numbers, the recordable area of the new CD is
(pi*29.25^2)(pi*11.5^2) = 2271.199 mm^2.
Dividing these numbers we find that the new CD has an area 2271.199/9084.805
= 0.25 of the old.
However, given that we're using DVD tech on the hardware layer, we can
store 4.6 GB = 4939212390 bytes after ECC instead of just 700 MB =
734003200 bytes. This is an increase of 6.72 times the old format.
Multiplying these numbers, the total capacity of the new CD is 0.25 * 6.72
= 1.68 times the old.

Since a 700 MB CD is equivalent to 80 minutes of audio, we then get a "base
capacity" of 80 * 1.68 = 134.40 minutes, and for the various formats the
following capacities:
Format A: 134.4 * 2 = 269 minutes
Format B: 134.4 / 1.125 = 120 minutes
Format C: 134.4 / 0.233 = 577 minutes
Format D: 134.4 / 0.023 = 5768 minutes
2: 100minute CD
For the sake of simplicity, we'll fix the inner radius at 10 mm because
anything less becomes difficult to handle. Then we'll calculate for each
format.
First, we need to create a formula that inputs capacity and outputs outer
radius size. Since we're dealing with fractions we can then plug in the
various "capacity numbers" found above.
D = (pi*x^2)(pi*10^2)
= pi*x^2  314
D + 314 = pi*x^2
(D + 314) / pi = x^2
x = sqrt( ( D + 314) / pi )
( x formula here)
As we know, D = 9084.805 for an ordinary CD at 80 minutes. To scale to 100
minutes, D = 9084.805*1.2 = 10901.766. But this is at old tech capacity, and
to compensate for the new tech, we divide by 6.72 (from 1:) and get
D_equiv = 1622.2866
For the various formats.
Format A: D = 1622.2866 / 2 = 811.1433 x = 18.9 mm
Format B: D = 1622.2866 * 1.125 = 1825.072 x = 26.1 mm
Format C: D = 1622.2866 * 0.233 = 377.9928 x = 14.9 mm
Format D: D = 1622.2866 * 0.023 = 37.31259 x = 10.6 mm
Note Format D. This is less than a millimeter more than the inner radius.

[1] http://www.cdtesting.com/
[2] http://home.pacific.net.au/~gnb/maccdis/cd2.html