Problem

7. The area of the base of a hexagonal pyramid is \( \frac{24}{\tan 30^{\circ}} \mathrm{cm}^{2} \). Find its volume.

Answer

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Answer

3. Calculate the volume: V = \( \frac{1}{3} \times \frac{24}{\tan 30^{\circ}} \times r \)

Steps

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 = \( \frac{1}{3} \times \frac{24}{\tan 30^{\circ}} \times r \)

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