Step 1 :1. Calculate side length of hexagon base: a = \( \sqrt{\frac{24}{\tan 30^{\circ} \times \frac{3}{4}}} \)
Step 2 :2. Calculate the apothem: r = \( \frac{a}{2\tan(30^{\circ})} \)
Step 3 :3. Calculate the volume: V = \( \frac{1}{3} \times \frac{24}{\tan 30^{\circ}} \times r \)