

Many people are using this line in ncert to argue for 7.6 but this is only for intermediate steps, in the question the only intermediate step is finding the volume
length is given 9.0 which has 2 significant figures so the answer should be in 2 significant figure
now lets come to the intermediate step we need to retain 1 more digit, more than number of significant figure in 9.0 thus we need to retain 3 digits in volume calculation thus 9.0*9.0*9.0 give 729 cm^3 which has 3 digits and matches the rule thus we should keep 729
Now when we divide 5580/729 we get 7.6543209876543209876543209876543 to be exact and we need to round this off to two significant figues thus we get 7.7 g/cm^3 which should be correct answer and given in every other institute's answer key other than NTA