Based on the map, which industry was most prevalent in manchester? copper mining textiles shipbuilding metalware

You didn't provide a map, however, historically, Manchester was a city of Textile

It had the largest textile industry in the world because of its factories that would refine cotton and make textile that would be used for clothing or exported worldwide. This is why it was even called by historians as Cottonpolis since the factories with machines were the biggest buildings in the entire town, even greater than things like town halls.