The ratio of two numbers is the same as their quotient,
a:b = a/b.
But area and volume aren't dimensionless. Area isn't 6 and even isn't 6cm as you wrote, it is probably `6 cm^2.` Also volume is `1cm^3.`
So the answer is `(6 cm^2)/(1 cm^3)=6 cm^(-1).`