Hexa pyramid

The base of the regular pyramid is a hexagon, which can be described as a circle with a radius of 2 m. Find the volume of the pyramid to be 2.5 m high.

Correct answer:

V =  8.6603 m³

Step-by-step explanation:

$$\begin{gathered} r=2\text{m} \\ h=2.5\text{m} \\ {S}_1=\frac{\sqrt{3}}{4}\cdot r^2=\frac{\sqrt{3}}{4}\cdot 2^2=\sqrt{3}{\text{m}}^2\doteq 1.7321{\text{m}}^2 \\ S=6\cdot S_1=6\cdot 1.7321=6\sqrt{3}{\text{m}}^2\doteq 10.3923{\text{m}}^2 \\ V=\frac{1}{3}\cdot S\cdot h=\frac{1}{3}\cdot 10.3923\cdot 2.5=5\sqrt{3}=8.6603{\text{m}}^3 \end{gathered}$$

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