Hexagonal Pyramid Volume

The tops of the base of a regular hexagonal pyramid lie on a circle with a radius of 10 cm. The height of the pyramid is 12 cm. What is its volume?

Final Answer:

V =  1039.2305 cm³

Step-by-step explanation:

$$\begin{gathered} r=10\text{cm} \\ h=12\text{cm} \\ {S}_1=\frac{3}{2}\cdot \sqrt{3}\cdot r^2=\frac{3}{2}\cdot \sqrt{3}\cdot 10^2=150\sqrt{3}{\text{cm}}^2\doteq 259.8076{\text{cm}}^2 \\ V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 259.8076\cdot 12=600\sqrt{3}=1039.2305{\text{cm}}^3 \end{gathered}$$

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