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Volume_of_cube = side3 ⇒ side = 3√volume Surface_area_of_cube = 6 x side2 = 6 x (3√volume)2 = 6 x volume2/3
Let V=volume V^(1/3)=Side Length=S 6*S^2=Surface Area Surface Area=6*(Volume)^(2/3)
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If the total surface area is A square units, then the volume is (A/6)1.5 or (A/6)3/2 cubic units. Step by step: There are 6 faces so the area of each face is A/6 square units. Therefore, the face is s square with sides of length sqrt(A/6) units. And therefore, the volume is [sqrt(A/6)]3= (A/6)3/2 cubic units.
Since the cell has six sides, it must be a tetrahedron. Area = sqrt(3)*32 mm2 = 9*sqrt(3) mm2 Volume = 33/(6*sqrt(2)) So area/Volume = 9*sqrt(3)*6*sqrt(2)/33 mm = 2*sqrt(6) mm