Can the age of the universe be used to calculate the size of the
universe? For example, assume the universe is 15 billion years old. 
Since the universe cannot expand faster than the speed of light, does
this imply that the "radius" of the universe is 15 billion light
years?  And if so, can you use this measurement to calculate the
volume of the universe, like you can if you know the radius of a
sphere?

In an rough estimation your assumptions are true. If you want to find
out precise details of the modern cosmological theory this would
definitely go beyond the scale of an answer that can be given here.

So that´s what I´ve found out for you:

“ Astronomers believe that the Universe began with the Big Bang,some
10 - 20 billion years ago. So, the most distant objects that we can
see are about 10 - 20 billion light-years (= 1027 cm) away.”
form:
The Scale of the Universe
( http://casswww.ucsd.edu/public/tutorial/scale.html )

“The visible universe has a radius of about 15 billion light years
simply because the universe is about 15 billion years old. The light
from more distant objects simply has not had time to reach us. For
this reason everybody in the universe is at the middle of their own
visible universe about 15 billion light years in radius. The true size
of the universe has to be much larger than this though. How large
depends on whether the universe is open or closed, that is whether
there is enough matter in the universe to halt its expansion at some
point in the far distant future. If there is then the universe is
probably finite in size. The other possibility is that the universe
will keep expanding forever - this means the universe is probably
infinite in size. Whichever scenario is correct, it is clear that the
visible universe is only a minute speck in a far larger totality.”
from:
The Visible Universe
( http://www.anzwers.org/free/universe/universe.html )

“Q:
When I read about the estimant of the age of the universe I see a
paradox. Reports on NASA's site estimate telescopes like the HST can
see about 10 billion light years and the latest speed of the expansion
of the universe is about 300 kps. For the universe to be 10 billion
light years + in diameter it would take 10 trillion years to be that
size at that speed. Am I misunderstanding something?
A:
The universe is not expanding at a uniform rate, but for a rough
estimate we can assume that the most distant galaxies are rushing away
from us at the speed of light. There are about 30 million seconds in a
year, so at 300,000 km/sec the universe would expand by an amount
(30,000,000 sec ) X 300,000 km/sec = 9,000,000,000,000 km = 9 trillion
km = 1.5 light years. So in 10 billion years the universe would expand
to about 15 billion light years. “
from:
Chandra Ressources
(http://chandra.harvard.edu/resources/faq/cosmology/cosmology-15.html
)


“The simple answer is that the observable Universe is about 10 billion
light years in radius. That number is obtained by multiplying how old
we think the Universe is by the speed of light. The reasoning there is
quite straightforward: we can only see out to that distance from which
light can have reached us since the Universe began. (But see my note
marked * below).
We determine the age of the Universe in a number of ways. One is to
estimate the age of the oldest stars we see. Our knowledge of how
stars of a given size evolve with time is very good (based on what we
know about atomic and nuclear physics) so the major uncertainty here
is usually measuring how far away (and so how big) such stars are. The
standard method is to look for very small changes in the apparent
positions of the stars as the Earth moves around the Sun. (This effect
is called parallax). A second way to get an age for the Universe is to
try to figure out the time of the big bang itself. Here the method is
to use a series of techniques (based on how bright things appear to be
- like Cepheid variable stars - that we think we know the true
brightness of) to determine first the distance of the nearby galaxies,
then increasingly distant galaxies, until we have estimated distances
for many galaxies for which relative velocity measurements have been
made (using the Doppler red shift of features in their spectra). The
relative velocities we observe for distant galaxies have been largely
determined by the expansion of the Universe begun with the 'big bang'.
So, once we've determined how expansion velocity correlates with
distance for some range of distances, it's possible to extrapolate
back (with some assumptions) to calculate the instant of the big bang,
when all the matter in the Universe was at a single point.”
from:
Measuring the size of the Universe 
( http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/971124x.html )

Interesting in tis context is that the 
“amazing idea, that the universe could have expanded from one tiny
point, was not accepted by everyone. A radical group of cosmologists
at Cambridge, led by Fred Hoyle, came up with the steady state theory.
This said that there had been no Big Bang and that the universe had
always been roughly the size it is now, but that new matter was
spontaneously being created all the time and that this was the reason
that the universe was expanding.
As proof for their theory they had to find a place in the universe
where all the elements were formed. The steady state scientists made
the brilliant discovery that the intensely hot conditions in the
inside of stars formed all the elements that now make up our planet
and even ourselves. However, stars start with the basic fuel of
hydrogen. It seemed as if the Big Bang would be the only place hot
enough to have formed hydrogen, was this the first piece of evidence
for how the universe formed?”
form:
Stephen Hawking´s Universe
( http://www.psyclops.com/hawking/shu/shu2.html )


You´ll find a detailed quantum mechanical explanation at:
(  http://superstringtheory.com/cosmo/cosmo1a.html ) 
I have not cited this one because there too many formulas there.


Search Strategy
( ://www.google.de/search?sourceid=navclient&hl=de&querytime=M&q=size+universe+light+speed
)

This was a pretty good answer given the difficulty of the subject
matter.  I also liked everyone's comments.

Hi halejrb,

I wouldn't DARE to answer this, as it's way over my head.  However, I
thought these links might interest you:
http://www.physlink.com/Education/AskExperts/ae220.cfm "By what method
is the size (or volume) of the universe at the moment of the big bang
(or shortly thereafter) determined? Related to this, how is the size
of a black hole determined?"

http://online.itp.ucsb.edu/online/plecture/kirshner/ Taking Measure of
the Universe: How Big? How Old? How Do We Know? by Robert Kirshner,
Harvard University

http://imagine.gsfc.nasa.gov/docs/science/mysteries_l1/age.html How do
we measure the size and the age of the Universe?

Good luck!

Though this is very far from my areas of expertise, I noticed in
several of the references above that the estimated size seems to be
based on the speed of light and the farthest visible stars. Wouldn't
that presume we are at the center of the universe???
If we were not, and if it is expanding, as it is presumed by some
that, the distance to the edge would depend on which way we look?????

Good answer.  
I love these types of questions! Just another thought: we know that
the universe is expanding, but what volume/space is it expanding into
if there is no 'outside' to the universe?

bobthedispatcher this might shed a bit of light on your point:
"How far away from the center of the universe is the Milky Way ?
If it were not for modern cosmology, the observation by astronomers
that distant galaxies are moving away from us at higher and higher
speed would mean that we are located at the center of the universe.
But thanks to Einstein's theory of general relativity, which is the
basis for all of modern cosmology, we now know how to interpret the
apparent motion of distant galaxies. The answer, now, is that there is
no unique center to the universe at all.

The best way to see this is to take a balloon and put a few dots on
it. Blow the balloon up and watch as the dots move away from each
other. Which ever dot you would choose to identify as the Milky Way,
all of the other dots would seem to be moving away from it giving you
the illusion that your galaxy is at the center of the universe.

So, the answer to this question is that the Milky Way appears to be
sitting right at the center of the expansion of the universe, but the
universe itself has no center. "
http://itss.raytheon.com/cafe/qadir/q82.html

Of course if there is no center, it would be difficult to determine
the distance from that(non-existant) point, therefor we would have no
real point of reference to measure from, except our relative position,
which doesn't really answer the original question.  ???

Sort of like being adrift in the ocean, in a heavy fog, without
compass, or any electronic aids, and trying to determine where the
nearest land was.

Or indeed looking for a mute black cat in a coal cellar with the lights out!

I agree there is no "center" to the universe, at least not the 3
dimensional universe we can observe.  That's why the "dots on an
expanding balloon" is such a good analogy.  That's also the reason I
put the term "radius" in quotes in my question.  If you pick any point
on the balloon as the "center" of this two dimensinal balloon
universe, then the point opposite it on the other side of the balloon
becomes the farther observable location in this universe.  The
distance between these points is 1/2 the circumference of the balloon,
or in the example of the real universe, around 15 billion light years.
 It should be possible to "do the math" to figure out the volume for a
universe in which it is 15 billion light years between two farthest
points. I realize though that the universe is not really like the
surface of a balloon.  It's much more complicated than that and I
assume the math needed for answering the question is very complicated
too.
   I'm also aware though of the "Stickman" map of the known universe. 
Presumably, you can measure distance on this map and determine the
volume of the known universe.

re: halejrb-ga comment

Question:
 If your analogy of a balloon surface, as a 2 dimesional space is
used, then how can you have a volume (3 dimensional??)

I have a feeling that this may expand the scope of the original
question enormously, and probably way beyond what was desired.

But it is an interesting subject.

Hello bobthedispatcher.  You're right, I did switch from 2 dimensions
to 3 dimensions.  The balloon example is a good way of showing in two
dimensions how every point on the balloon can move away from every
other point as the balloon expands.  This is similar to the way every
galaxy is moving away from every other galaxy in the real 3
dimensional universe.  But the comparison is obviously not perfect. 
That's what I meant when I said the math gets more complicated when
you try to calculate the volume of a 3 D universe in which space
itself may be curved.  But even if the math is complex, given the fact
that the size of the universe is proportionate to the age of the
universe due to the speed of light, I think it should be possible to
calculate the size of the universe for any given age.  :-)

Have a look at this site which explains what the hubble constant is:

v = Ho * d
"Why such a heated debate over a single number? The Hubble Constant is
one of the most important numbers in cosmology because it is needed to
estimate the size and age of the universe. "
http://www.astro.washington.edu/astro101v/labs/hubblelaw/hubblelaw.html

Just last week, the shape of the universe was discussed on the radio
program "Science Friday".

"Then, we'll turn our attention to the Big Questions in the universe
-- where'd it come from? Where's it going? How'd it get to be the way
that it is? Guest host David Kestenbaum talks with cosmologist Janna
Levin about her work, cosmology in general, and her book, "How the
Universe Got Its Spots: Diary of a Finite Time in a Finite Space." "
http://www.sciencefriday.com/pages/2002/Jul/hour2_071202.html
http://www.amazon.com/exec/obidos/ASIN/0691096570/sciencefriday

Related Links:

"Age of the Universe 
There are at least 3 ways that the age of the Universe can be
estimated. I will describe
The age of the chemical elements. 
The age of the oldest star clusters. 
The age of the oldest white dwarf stars."
http://www.astro.ucla.edu/~wright/age.html (very technical site)

Cosmology: The Study of the Universe
http://map.gsfc.nasa.gov/m_uni.html (this link was referenced by
others)

"An Age Crisis?
If we compare the two age determinations, there is a potential crisis.
If the universe is flat, and dominated by ordinary or dark matter, the
age of the universe as inferred from the Hubble constant would be
about 9 billion years. The age of the universe would be shorter than
the age of oldest stars. This contradiction implies that either 1) our
measurement of the Hubble constant is incorrect, 2) the Big Bang
theory is incorrect or 3) that we need a form of matter like a
cosmological constant that implies an older age for a given observed
expansion rate."
http://map.gsfc.nasa.gov/m_uni/uni_101age.html

Luke Skywalker to C-3PO: "If there is a bright center to the universe,
you're on the planet it's farthest from."

If only George Lucas would tell us where to locate Tatooine, many
cosmological questions would be answered. ;-)

This is turning into a discussion group, not an answer!
:}  :}

Could be there are no answers, just theories (and guesses)

It isn't the size of the universe that matters, it's the interaction
between the planets. :)