Space diagonal

The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.

Result

L =  5625 mm2
S =  33750 mm2
V =  421875 mm3

Solution:

d=129.91 mm  d2=a2+a2+a2 d2=3a2  d=3a  a=[d/3]=[129.91/3]=75 mm  L=a2=752=5625 mm2d=129.91 \ \text{mm} \ \\ \ \\ d^2=a^2+a^2+a^2 \ \\ d^2=3a^2 \ \\ \ \\ d=\sqrt{ 3 } a \ \\ \ \\ a=[ { d/ \sqrt{ 3 } } ]=[ { 129.91/ \sqrt{ 3 } } ]=75 \ \text{mm} \ \\ \ \\ L=a^2=75^2=5625 \ \text{mm}^2
S=6 L=6 5625=33750 mm2S=6 \cdot \ L=6 \cdot \ 5625=33750 \ \text{mm}^2
V=a3=753=421875 mm3V=a^3=75^3=421875 \ \text{mm}^3



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