Step 1: Recall how nuclear size depends on mass number.
Every nucleus follows the empirical rule that its radius grows with the cube root of the mass number, written as \[ R = R_0 A^{1/3} \] where $R_0$ is the same constant for all nuclei.
Step 2: Set up a ratio so $R_0$ cancels.
Comparing the aluminium nucleus (call it 1) with the unknown nucleus (call it 2), we divide one relation by the other to get \[ \frac{R_1}{R_2} = \left(\frac{A_1}{A_2}\right)^{1/3} \]
Step 3: Put in the known numbers.
For aluminium $A_1 = 27$ and $R_1 = 3.6$ fm, while the unknown has $R_2 = 4.8$ fm, so \[ \frac{3.6}{4.8} = \left(\frac{27}{A_2}\right)^{1/3} \] which simplifies to $\frac{3}{4} = \left(\frac{27}{A_2}\right)^{1/3}$.
Step 4: Cube both sides to free $A_2$.
Cubing gives \[ \frac{27}{64} = \frac{27}{A_2} \] and matching the numerators tells us directly that $A_2 = 64$.
Step 5: Use the neutron relation.
The number of neutrons in any nucleus is the mass number minus the atomic number, that is $N = A - Z$.
Step 6: Compute the neutron count.
With $A = 64$ and $Z = 29$, we find $N = 64 - 29 = 35$. So the nucleus carries 35 neutrons, matching option 2.
\[ \boxed{N = 35} \]