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.

Result

V =  2.165 m3

Solution:

r=1 m h=2.5 m  S1=34⋅ r2=34⋅ 12≐0.433 m2 S=6⋅ S1=6⋅ 0.433≐2.5981 m2  V=13⋅ S⋅ h=13⋅ 2.5981⋅ 2.5≐2.1651≐2.165 m3r=1 \ \text{m} \ \\ h=2.5 \ \text{m} \ \\ \ \\ S_{1}=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ r^2=\dfrac{ \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=\dfrac{ 1 }{ 3 } \cdot \ S \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 2.5981 \cdot \ 2.5 \doteq 2.1651 \doteq 2.165 \ \text{m}^3

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