# Q & A: Volume of a balloon

Q:
what is the equation for the volume of an air balloon
- alexsandra flores (age 18)
lancaster pa
A:
Hi Alexsandra,

If we assume that an air balloon is a sphere, then the volume of the balloon is:

V = (4/3) * Pi * R^3

where R is the radius of the balloon. The volume might be a bit bigger if it bulges on one side (near the nozzle, for example). Hot-air balloons people use to fly have shapes quite different from a sphere.

If we assume the ballon is a cylinder, then the volume is

V = L * Pi * R^2

where L is the length and R is the radius of a circular cross-section.

Balloons come in all sorts of shapes and sizes. Some are twisty. Some are heart-shaped (especially around Valentine's day). I remember seeing a gigantic one at a hot-air balloon festival that was shaped and decorated like the rabbit they use as a mascot for selling batteries. I'm afraid we cannot give you formulas for every kind of balloon you may come across.

James and Tom

(published on 10/22/2007)

## Follow-Up #1: Volume of balloon

Q:
how can we find the volume of a irregular shape balloon?
- raghu vamshi (age 18)
india
A:
Method 1.  Fill the balloon with water, then weigh it.  The volume is then:
Volume (cm^3) = Weight(gm)/1(gm/cm^3), (neglecting the weight of the empty balloon.)

Method 2.  Fill the balloon with air.  Then, under water, let the air escape into an inverted bottle that has been filled with water.  Weigh the full bottle, then again with the air that has escaped from the balloon.  Use the same equation as in #1 where Weight = Weight(full)-Weight(not so full).

LeeH

(published on 10/22/2007)

## Follow-Up #2: How to measure a big balloon

Q:
I have a large balloon For high altitude research that is about the size of a school bus I need to know exactly what the volume of the balloon is in order to know how much helium is in it and how much lift it will provide. Any thoughts?
- Patrick (age 50)
Louisville, KY, USA
A:
You could just fill the balloon and measure the lift, but maybe you don't have a good place to store it filled while you build the other equipment, and you certainly don't want to throw out the helium. You could fill it with dry nitrogen, measuring the amount needed from the change in pressure of the tanks as they empty, and the calibrated tank volume. Maybe you could get help from someone emptying a swimming pool around this time of year. You could fill the balloon in a pool where the amount of water being drained off was being measured. Keeping the balloon underwater and measuring the water displaced as it fills would give an accurate volume measurement.

Mike W.

(published on 10/25/2011)