Yes, you should put a lightbulb exactly in the middle of a big round balloon. I normally like to use 100 watt lightbulbs around the house, but that might get too hot inside the balloon. So I think a 1 watt light bulb would be better. And 1 is a nice round number. It should be a perfect light bulb, so that it actually sends out 1 watt of energy.
Maybe we should make the light bulb round too, and send out the energy equally in all directions. That would be perfect. And we will have perfect air in our balloon too, so that the air does not block any of the light from getting through. No LA smog in our balloon!
I’m wondering just how big our big balloon is. Maybe it has a radius of 1 meter. Maybe it is really big and has a radius of 1 mile! I just don’t know. 
I was thinking about how much warming the light bulb would cause on the balloon. If the inside of the balloon does not reflect the light, then I suppose that the balloon will get 1 watt of heat, no matter how big it is. All the energy from the light bulb will travel straight out and hit the inside of the balloon, and heat it. So the amount of energy that heats the balloon is a constant 1 watt, as long as our light bulb is turned on.
But I guess that does not mean that regardless of size, a specific sized piece of the balloon gets the same amount of heat. If we look at 1 square meter of surface area of the balloon, and ask how much heat it gets if the balloon radius is 1 mile, then we have a math issue. But it seems obvious that it is less heating per square meter than it would be if the radius were only a meter. That is, assuming that a balloon of 1 meter radius really has at least 1 square meter of surface area.
I shall look on the internet and see if I can find out how much surface area a balloon with a radius of 1 meter really has. BRB!
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I’m back! I found it, here it is: Surface Area of a Sphere = 4 pi r 2
I found it at this web site, where it has other stuff too.
http://www.math.com/tables/geometry/surfareas.htm
Or you can look here:
http://mathcentral.uregina.ca/QQ/database/QQ.09.99/wilkie1.html
So, 4 is a number that is always there, r is the radius.
Pi seems to be a number that no can write down exactly. But it is about 3.14159 or so. Using it in math might be easier if we just rounded it off to 3. It would be even easier if we did not substitute a number for it at all, just let it be pi!
So, back to the question of whether or not a balloon with a radius of 1 meter has a surface area of at least a square meter or not. Well, if we apply the formula, and say that pi = 3, then we get:
Surface Area of our Sphere = 4 pi r 2 = 4*3*(1m) 2 = 12m 2 , so the area is about 12 square meters, certainly more than one.
Now we are prepared to figure out how much power from this 1 watt bulb each square meter really gets. If the surface area inside this balloon is about 12 square meters ( 12m 2 ) then each square meter of the 12 would get its own share, or 1/12 of a watt. True, we rounded of pi a bit, so the answer is not exact. But this isn’t the bank. We don’t need to be exact. We need to be sure we are right, which means we should be able to figure it out in our head, or at the very most, on a napkin with a pen or pencil. Stated another way, I am not looking for precision, I am looking for certainty that I’m about right.
So this brings me to Dave’s rule #1: Don’t bet a million dollars on anything you can’t figure out in your head or on a napkin. (Don’t be watching for Dave’s rule #2. All my rules are ‘Dave’s rule #1′.)
