Hexagon rotation

A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?


V =  226.195 cm3


a=6 cm k=60/180=130.3333 h=a2(a/2)2=62(6/2)23 3 cm5.1962 cm S1=π h2=3.1416 5.1962284.823 cm2 V1=S1 a=84.823 6508.938 cm3 V2=1/3 S1 (a/2)=1/3 84.823 (6/2)84.823 cm3 V=k (V2+V1+V2)=0.3333 (84.823+508.938+84.823)226.1947226.195 cm3a=6 \ \text{cm} \ \\ k=60/180=\dfrac{ 1 }{ 3 } \doteq 0.3333 \ \\ h=\sqrt{ a^2-(a/2)^2 }=\sqrt{ 6^2-(6/2)^2 } \doteq 3 \ \sqrt{ 3 } \ \text{cm} \doteq 5.1962 \ \text{cm} \ \\ S_{1}=\pi \cdot \ h^2=3.1416 \cdot \ 5.1962^2 \doteq 84.823 \ \text{cm}^2 \ \\ V_{1}=S_{1} \cdot \ a=84.823 \cdot \ 6 \doteq 508.938 \ \text{cm}^3 \ \\ V_{2}=1/3 \cdot \ S_{1} \cdot \ (a/2)=1/3 \cdot \ 84.823 \cdot \ (6/2) \doteq 84.823 \ \text{cm}^3 \ \\ V=k \cdot \ (V_{2}+V_{1}+V_{2})=0.3333 \cdot \ (84.823+508.938+84.823) \doteq 226.1947 \doteq 226.195 \ \text{cm}^3

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Please specify the variables used ...using a figure will be great

Body consist of 3 parts: cone + cylinder + cone.


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