# Shape Volume Calculations

#### MathsDummy

So I'm realising I should have paid more attention in school, because I'm sure this would be a lot easier.

Anyway, I work in the metal industry and am constantly having to go to an online metal weight calculator to figure out information I need. That'd be fine if the internet speed where I work wasn't essentially dial up! Using a calculator is much faster or even better, a spreadsheet I could enter details into. I therefore need to know how to work out the volume of different shaped pieces of metal so I can multiply it by the density and get the overall weight of that item.

Square and rectangular shaped items are easy... length x width x height x density.
It's cylindrical, hollow and odd-shaped items that I'm struggling with.

I'd like to know how to calculate the volume of...

Solid Cylindrical items
Hollow Cylindrical items (tube/pipe) the metal weight only not the volume the inside can carry
Hollow square/rectangular items
T shape items

Any help would be greatly appreciated.

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#### skipjack

Forum Staff
For a metal pipe, you need to find the interior volume accurately, so you need an accurate figure for the internal diameter. You also need the external diameter of the pipe.

Suppose, for example, that the internal diameter is 1.5 cm, the external diameter is 1.75cm, and you calculate that the interior volume is 900 cmÂ³. Now multiply that by (1.75/1.5)Â². The result is 1225 cmÂ³. By subtraction, the volume of the metal is 325 cmÂ³.

#### MathsDummy

Could you dumb that down for me please?

Generally, in this industry we use mm and not cubic measurements.

If I was to work this out on a calculator. How would I do it? Much like the example I gave for sold square/rectangular items.

#### MathsDummy

For a metal pipe, you need to find the interior volume accurately, so you need an accurate figure for the internal diameter. You also need the external diameter of the pipe.

Suppose, for example, that the internal diameter is 1.5 cm, the external diameter is 1.75cm, and you calculate that the interior volume is 900 cmÂ³. Now multiply that by (1.75/1.5)Â². The result is 1225 cmÂ³. By subtraction, the volume of the metal is 325 cmÂ³.
Ok so after some googling I get it... kind of. So I work out the volume of the inside dimension which is... From your example...

Volume = Pie (can't find the character on an iPhone) x radius x height.
V = pie (0.75cm) squared x height (10cm for example)
V = 5.625cm pie
V = 17.67cm cubed

So from your example to find the pipe volume is then...

17.67cm cubed x (1.75/1.5) squared and then subtract the 17.67cm cubed?

Forum Staff
Yes.

#### OTheB

Why not put it in a square prism box full of water then measure how much the water rises? If for instance you have a container 10m by 10m then put in your object then let's say the water rises by 1m. That means the volume of your object is equal to 10x10x1m which is 100m^3

This is the only reasonable way of finding the volume of really iregular or overly compund shapes.

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