Is the word volume the same in Brazilian and European Portuguese?

No

While the spelling, grammar, and core meaning of "volume" are identical in both Brazilian and Continental Portuguese, the answer is "No" because there is a difference in typical usage and pronunciation.

In terms of usage, while "volume" is perfectly understood in Portugal, it is much more natural for a Portuguese person to use the word "som" (sound) when referring to audio levels. Additionally, the pronunciation differs significantly: Brazilian Portuguese tends to have more open vowels and a syllable-timed rhythm, whereas Continental Portuguese features more closed vowels and a stress-timed rhythm.

Brazilian Portuguese Example Sentences

1. Abaixe o volume da televisão, por favor. (Turn down the TV volume, please.)
2. O volume de vendas aumentou muito este mês. (The sales volume increased a lot this month.)
3. Este é o primeiro volume da coleção. (This is the first volume of the collection.)
4. O volume de água no reservatório está baixo. (The volume of water in the reservoir is low.)
5. O meu cabelo está com muito volume hoje. (My hair has a lot of volume today.)

Portuguese (Continental) Example Sentences

1. Abaixa o som da televisão, por favor. (Turn down the TV sound, please.)
2. O volume de vendas aumentou muito este mês. (The sales volume increased a lot this month.)
3. Este é o primeiro volume da coleção. (This is the first volume of the collection.)
4. O volume de água no reservatório está baixo. (The volume of water in the reservoir is low.)
5. O meu cabelo está com muito volume hoje. (My hair has a lot of volume today.)