Answer is: there are nine orbitals in the n = 3 shell, 3² = 9.
Principal quantum number (n) describes the size of the orbital. There are one s orbital (angular quantum number l=0), three p orbitals (angular quantum number l=1 and magnetic quantum number m = -1,0,+1) and five d orbitals (angular quantum number l=2 and magnetic quantum number m = -2,-1,0,+1,+2).