   SEARCH HOME Math Central Quandaries & Queries  Relating volume (capacity) to inches in height of a cylinder of given dimensions I have a cylindrical polyethylene rain barrel 23" in diameter and 35" high. If I've calculated correctly thus far, its volume is: 14, 547.49 cubic inches (or 8.418686 cubic feet or 0.31 cubic yards) and could, ideally, contain 62.6 gallons of rain water whose weight would be 525.32 lbs. (62.4 lbs./cubic foot X 8.418686). I'm having difficulty relating inch depth markings on the side of the barrel to volume capacity; i.e., how many inches in depth in a cylinder of the size given would = how many gallons (or quarts) of water. The barrel stands upright on its end and is, thus, 35" high when oriented in this fashion, much as a 55-gallon oil drum appears when similarly stowed. If you could give me some help with this calculation, I'd be most grateful. Dan Hi Dan.

I agree with all your calculations. When the barrel is empty, there are zero gallons and the "height" of the water is 0 inches. When the barrel is full, there are 62.6 gallons in it and the height is 35 inches. So you have a simple ratio.

Every 35/62.6 = 0.56 inches corresponds to 1 gallon.

Every inch corresponds to 62.6/35 = 1.8 gallons.

So you can read off the inch depth markings and multiply by 1.8 to get your gallons.

Or you can mark off the 10 gallon line at 5.6 inches, the 20 gallon line at 11.2 inches, and so on.

Hope this helps,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.