In general the first thing that happens is to decide if the cable size will be set by voltage drop (resistance, or  perhaps resistance plus inductance) or  thermal consideration (i.e. the copper in the cable getting too hot.) If the latter, then the cable rating tables are your friend as folk have spent many years measuring cables of many sizes in many configurations, and even then the one you want to use is often not there and you have to mutter 'it is a bit like' and use the figures for another case.

Here follow some pretty terrible rounding errors and rules of thumb for the whistle through teeth manual calculation.

1) Step 1 verify voltage drop with the rule of 16 (or 19)  the resistance of a 1mm2 cross section of copper 1m long, is 16 milliohms.
Each of the your 3 phase cores has 160A to carry, but they are in balance so there is no neutral 'return path' voltage drop to consider.
Lets assume we can take  5% voltage drop (for easy sums)  on each phase we can drop 12V (being 5% of 240...)
to drop 12V at 160A we need 0.075 of an ohm - 75 milliohms. your cable run is 10m, so your maximum cable resistance - assuming heating was not  an issue would be 75/16  so 4.6mm2 .

But a quick look at current ratings tell us that if that 160A continues for more than a few seconds,  a 4.6mm2 cable would be toast.
YOUR EXAMPLE IS NOT VOLTAGE DROP LIMITED (but a different job with significantly longer cable run may well be)

2) step 2 lets size the cable based on it getting hot.. The tables in the back of the book look similar to those in this datasheet.

https://www.elandcables.com/media/38889/bs-6724-copper-conductor-multi-core-swa-lszh-basec-0-6-1kv-cable.pdf

Flick to page 4, current ratings ...

Now decide which options are the cheapest (usually thinnest) cable where the rating is above your design current. Now 35mm2 just makes it on a tray (3phase cable so 4th column.) Now if any of your cable route was clipped to a wall, then as the cooling is not as good as open tray, then you'd be in colun 2, and and you would need the next size up...

Note the small print that these tables assume

Air ambient temperature: 30ºC
Ground ambient temperature: 20ºC
Conductor operating temperature: 90ºC (so a sixty degree rise once steady state is reached )

If you want the copper not to get to 90C you need a bigger cable, if the air temp is a lot lower you may be able to tolerate a thinner cable. If the cooling airflow is not so cold due to other cables running hot alongside, then the cable needs to go up a size etc.

Tadah.

Mike.

In general the first thing that happens is to decide if the cable size will be set by voltage drop (resistance, or  perhaps resistance plus inductance) or  thermal consideration (i.e. the copper in the cable getting too hot.) If the latter, then the cable rating tables are your friend as folk have spent many years measuring cables of many sizes in many configurations, and even then the one you want to use is often not there and you have to mutter 'it is a bit like' and use the figures for another case.

Here follow some pretty terrible rounding errors and rules of thumb for the whistle through teeth manual calculation.

1) Step 1 verify voltage drop with the rule of 16 (or 19)  the resistance of a 1mm2 cross section of copper 1m long, is 16 milliohms.
Each of the your 3 phase cores has 160A to carry, but they are in balance so there is no neutral 'return path' voltage drop to consider.
Lets assume we can take  5% voltage drop (for easy sums)  on each phase we can drop 12V (being 5% of 240...)
to drop 12V at 160A we need 0.075 of an ohm - 75 milliohms. your cable run is 10m, so your maximum cable resistance - assuming heating was not  an issue would be 75/16  so 4.6mm2 .

But a quick look at current ratings tell us that if that 160A continues for more than a few seconds,  a 4.6mm2 cable would be toast.
YOUR EXAMPLE IS NOT VOLTAGE DROP LIMITED (but a different job with significantly longer cable run may well be)

2) step 2 lets size the cable based on it getting hot.. The tables in the back of the book look similar to those in this datasheet.

https://www.elandcables.com/media/38889/bs-6724-copper-conductor-multi-core-swa-lszh-basec-0-6-1kv-cable.pdf

Flick to page 4, current ratings ...

Now decide which options are the cheapest (usually thinnest) cable where the rating is above your design current. Now 35mm2 just makes it on a tray (3phase cable so 4th column.) Now if any of your cable route was clipped to a wall, then as the cooling is not as good as open tray, then you'd be in colun 2, and and you would need the next size up...

Note the small print that these tables assume

Air ambient temperature: 30ºC
Ground ambient temperature: 20ºC
Conductor operating temperature: 90ºC (so a sixty degree rise once steady state is reached )

If you want the copper not to get to 90C you need a bigger cable, if the air temp is a lot lower you may be able to tolerate a thinner cable. If the cooling airflow is not so cold due to other cables running hot alongside, then the cable needs to go up a size etc.

Tadah.

Mike.