# Volume of a cylinder: liquid vs solid

Apologies if this question is too much high school maths for the site, I'm a refugee from the webmaster stack site, and thought I might find some help here.

The question concerns candle making (in the real world). I'm thinking of purchasing some large pillar candle moulds from a company in Australia (can't find the right size anywhere else) and I need to check that I can melt enough wax to fill a single mould in one go and if not figure out what size boiler I should buy.

Problem is wax is sold in dry weights and the volume is calculated in, well, liquid volume. I don't know how to translate between the two.

• Volume is V = πr2h.
• Mould is 100mm diameter and 241mm tall
• = 7574285.714285708 Cubic millimeters
• = 7.574285714 cubic liters.

So, the problems are these:

1. Basically the result doesn't make complete sense to me - it shouldn't be that large! Have I done the conversion incorrectly or is there a difference that I'm unaware of between American and British volume calculations (I'm a Brit).
2. Candle wax is sold in dry kilograms, I've seen various conversion charts online, but they often seem to be guess work. Is there a simple formula for converting a dry weight of a solid into it's resulting liquid volume.

Apologies if this is too simple or the solution is obvious, and thanks in advance for your help.

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"Refugee"? Are they persecuting your people over at webmasters.SE? :) Anyway, first off, WolframAlpha is a quick-and-easy sanity check that disagrees with your calculation of the cylinder's volume. Second, the conversion from solid to liquid volume is a question of physics, not mathematics. Most materials expand when melting, but water expands when freezing. You'll have to look up the thermal expansion properties of wax. – Rahul May 28 '12 at 19:26
Usually you need to know the density of a material to convert between mass and volume. There is also a difference between the densities of solid and liquid forms of a substance. More commonly solid is slightly heavier per unit volume, but ice floats on water, so... – Jyrki Lahtonen May 28 '12 at 19:26
Whoops, Jyrki is right; I didn't notice you need to convert from mass to volume. For that you need to know the density of wax; density is mass divided by volume, so volume is mass divided by density. – Rahul May 28 '12 at 19:29
Tip 1: the radius is half the diameter. Tip 2: the dry weight of a solid is the same as the wet weight. – TonyK May 28 '12 at 19:31
To a first approximation, you can probably assume the thermal expansion to be negligible. Just look up the density of wax, and divide the mass by it to get the volume. Be careful about units. For a cylinder of your given measurements, for example, assuming paraffin wax has a density of 0.93 g/cc, you'll need 1.76 kg to fill it. – Rahul May 28 '12 at 19:35

As pointed out in comments, the computation is off by $4$ due to the diameter being twice the radius. A cylinder of radius $50/1000$ meters and height $241/1000$ meters has volume of about $1.89$ liters. Using the wax density of $930$ kg/L yields $1.76$ kg.