To find the volume of water discharged by the pipe in half an hour, we can use the following steps:

1. Calculate the cross-sectional area of the pipe:

The diameter of the pipe is given as 2.4 cm. We first need to convert this into meters: $\text{Diameter} = 2.4 \, \text{cm} = 0.024 \, \text{m}$

The radius $r$ of the pipe is half of the diameter: $r = \frac{0.024}{2} = 0.012 \, \text{m}$

The cross-sectional area $A$