Hexagonal pyramid

The pyramid's base is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.

Final Answer:

V =  2.17 m³

Step-by-step explanation:

$$\begin{gathered} h=2.5\text{m} \\ r=1\text{m} \\ a=r=1\text{m} \\ n=6 \\ S=n\cdot \frac{\sqrt{3}}{4}\cdot a^2=6\cdot \frac{\sqrt{3}}{4}\cdot 1^2\doteq 2.5981{\text{m}}^2 \\ V=\frac{1}{3}\cdot S\cdot h=\frac{1}{3}\cdot 2.5981\cdot 2.5=2.17{\text{m}}^3 \end{gathered}$$

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