Octahedron

All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.

Result

S =  124.708 cm2
V =  101.823 cm3

Solution:

d=6 S1=3/4 d2=3/4 62=9 315.5885 S=8 S1=8 15.5885=72 3124.7077=124.708 cm2d = 6 \ \\ S_{ 1 } = \sqrt{ 3 }/4 \cdot \ d^2 = \sqrt{ 3 }/4 \cdot \ 6^2 = 9 \ \sqrt{ 3 } \doteq 15.5885 \ \\ S = 8 \cdot \ S_{ 1 } = 8 \cdot \ 15.5885 = 72 \ \sqrt{ 3 } \doteq 124.7077 = 124.708 \ cm^2
V=2/3 d3=2/3 63=72 2101.8234=101.823 cm3V = \sqrt{ 2 }/3 \cdot \ d^3 = \sqrt{ 2 }/3 \cdot \ 6^3 = 72 \ \sqrt{ 2 } \doteq 101.8234 = 101.823 \ cm^3



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