What is the volume of the cube if the diagonal is 1?

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justaguide eNotes educator | Certified Educator

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The diagonal of a cube is given as sqrt (3L^2), where L is the length of the side.

We know that the diagonal is 1.

=> 1 = sqrt (3L^2)

=> 1^2 = 3L^2

=> L^2 = 1/3

=> L = sqrt( 1/3)

The volume of a cube is L^3

=> [sqrt (1/3)]^3

=> (1/3) sqrt (1/3)

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hala718 eNotes educator | Certified Educator

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neela | Student

A cube is a regular prism which has  a square top, bottom and lateral surfaces with equal length, width and height.

If the side of the cube is x, then its diagonal d is given by:

d = x^2+x^2+x^2 = 3x^2.

So , if diagonal d= 1, then 1= 3x^2 => x= sqrt(1/3) is the side of the cube.

So the volume of the cube = x^3 = (sqrt(1/3)}^3 = (1/3^3/2)= 1/sqrt27 = 0.19245 cubic units.

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