Cube diagonals

Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.

Result

a =  3 cm
u1 =  4.243 cm
u2 =  5.196 cm

Solution:

V=27 cm3 a=V3=273=3=3  cm V = 27 \ cm^3 \ \\ a = \sqrt[3]{ V} = \sqrt[3]{ 27 } = 3 = 3 \ \text{ cm }
u1=2 a=2 3=3 24.2426=4.243  cm u_{ 1 } = \sqrt{ 2 } \cdot \ a = \sqrt{ 2 } \cdot \ 3 = 3 \ \sqrt{ 2 } \doteq 4.2426 = 4.243 \ \text{ cm }
u2=3 a=3 3=3 35.1962=5.196  cm u_{ 2 } = \sqrt{ 3 } \cdot \ a = \sqrt{ 3 } \cdot \ 3 = 3 \ \sqrt{ 3 } \doteq 5.1962 = 5.196 \ \text{ cm }



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