Hexa pyramid

The base of the regular pyramid is a hexagon, which can be described by a circle with a radius of 1 m. Find the volume of the pyramid 2.5 m high.

Correct result:

V =  2.1651 m³

Solution:

$$\begin{gathered} r=1\text{ m } \\ h=2.5\text{ m } \\ {S}_1={\displaystyle \frac{\sqrt{3}}{4}}\cdot r^2={\displaystyle \frac{\sqrt{3}}{4}}\cdot 1^2\doteq 0.433{\text{m}}^2 \\ S=6\cdot S_1=6\cdot 0.433\doteq 2.5981{\text{m}}^2 \\ V={\displaystyle \frac{1}{3}}\cdot S\cdot h={\displaystyle \frac{1}{3}}\cdot 2.5981\cdot 2.5=2.1651{\text{m}}^3 \end{gathered}$$

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