Hexagon cut pyramid

Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.

Result

V =  4593.916 cm3

Solution:

a1=30 cm a2=12 cm s=41 cm  S1=3 3/2 a22=3 3/2 122=216 3 cm2374.123 cm2 S2=3 3/2 a22=3 3/2 122=216 3 cm2374.123 cm2  x=s2(a1a2)2=412(3012)2=1357 cm36.8375 cm  h2=x a2/(a1a2)=36.8375 12/(3012)24.5583 cm h1=x+h2=36.8375+24.558361.3958 cm  V1=S1 h1/3=374.123 61.3958/37656.5266 cm3 V2=S2 h2/3=374.123 24.5583/33062.6107 cm3 V=V1V2=7656.52663062.61074593.916=4593.916 cm3a_{ 1 } = 30 \ cm \ \\ a_{ 2 } = 12 \ cm \ \\ s = 41 \ cm \ \\ \ \\ S_{ 1 } = 3 \cdot \ \sqrt{ 3 }/2 \cdot \ a_{ 2 }^2 = 3 \cdot \ \sqrt{ 3 }/2 \cdot \ 12^2 = 216 \ \sqrt{ 3 } \ cm^2 \doteq 374.123 \ cm^2 \ \\ S_{ 2 } = 3 \cdot \ \sqrt{ 3 }/2 \cdot \ a_{ 2 }^2 = 3 \cdot \ \sqrt{ 3 }/2 \cdot \ 12^2 = 216 \ \sqrt{ 3 } \ cm^2 \doteq 374.123 \ cm^2 \ \\ \ \\ x = \sqrt{ s^2-(a_{ 1 }-a_{ 2 })^2 } = \sqrt{ 41^2-(30-12)^2 } = \sqrt{ 1357 } \ cm \doteq 36.8375 \ cm \ \\ \ \\ h_{ 2 } = x \cdot \ a_{ 2 }/(a_{ 1 }-a_{ 2 }) = 36.8375 \cdot \ 12/(30-12) \doteq 24.5583 \ cm \ \\ h_{ 1 } = x+h_{ 2 } = 36.8375+24.5583 \doteq 61.3958 \ cm \ \\ \ \\ V_{ 1 } = S_{ 1 } \cdot \ h_{ 1 }/3 = 374.123 \cdot \ 61.3958/3 \doteq 7656.5266 \ cm^3 \ \\ V_{ 2 } = S_{ 2 } \cdot \ h_{ 2 }/3 = 374.123 \cdot \ 24.5583/3 \doteq 3062.6107 \ cm^3 \ \\ V = V_{ 1 }-V_{ 2 } = 7656.5266-3062.6107 \doteq 4593.916 = 4593.916 \ cm^3







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Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.