The solution is as follows:
Volume of a rod = πr²h
Volume = π(1.3×10⁻⁶ m/2)²(2.4×10⁻⁶ m)
Volume = 3.186×10⁻¹⁸ m³
Since 1 m³ = 1,000 L, the volume is equivalent to 3.186×10⁻¹⁵ L.
0.0051 mol/L * 3.186×10⁻¹⁵ L * 6.022×10²³ molecules/mole = 9,784,906.92 molecules