relation between volume, diagonal of cube
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let the digonal of a cube = 1cm
as we know diagonal of a cube(D)=√3a
where ' a ' is the side of a cube .
1 = √3a
a = 1/√3
a = 1/√3 × √3 /√3
a = √3 / 3
volume of cube = ( a )^3
= (√3/3)^3
= 3√3 / 27
=√3 / 9
=√3/9 × 1.
here,we can observe that,
volume of a cube=√3/9×diagonal of a cube
_________________________
Your Answer: V = √3 / 9 D
_________________________
as we know diagonal of a cube(D)=√3a
where ' a ' is the side of a cube .
1 = √3a
a = 1/√3
a = 1/√3 × √3 /√3
a = √3 / 3
volume of cube = ( a )^3
= (√3/3)^3
= 3√3 / 27
=√3 / 9
=√3/9 × 1.
here,we can observe that,
volume of a cube=√3/9×diagonal of a cube
_________________________
Your Answer: V = √3 / 9 D
_________________________
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