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Think of it as the difference in moment of inertias for two solid cubes. Calculate the moment of inertia of a solid cube with dimensions equal to the inner dimensions of your hollow cube. Then calculate the moment of inertia of a solid cube with dimensions equal to the outer dimensions of your hollow cube. Subtract the moment of inertia of the inner dimensions from the moment of inertia of the outer dimensions to get the moment of inertia of what's left. Same concept applies to finding the area of a thin-walled circle. Outer area - inner area = total area. Outer moment of inertia - inner moment of inertia = total moment of inertia.

This approach won't work however if you're considering hollow shell - a cube with walls of zero thickness.

If the axis of rotation goes through the cube center, perpendicular to one of its walls, first calculate moment of inertia of the wall that the axis passes through (let's call it Ia).

For all equations below d equals surface density(mass per unit of area) and a is length of cube's side.

Ia= d * a4 / 6

Then you have to calculate moments of inertia of four walls parallel to the axis.

This will be Ib=4 * Iwall=4*d*a4/3.

Total moment of the shell will be then:

I=2*Ia+Ib=1.5*d*a4.

If the axis is through the center and ┴ one face, I = (m/6)*[a² - (a-t)²], or

I = (m/6)(2at - t²) for any value of t, however small.

Source: CRC Std Math Tables

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To find the density of the cube material, divide the mass of the cube by its volume. You would first need to know the volume of the cube to calculate its density accurately. If the volume of the cube is 8cm³, then the density would be 96g/8cm³ = 12g/cm³.


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Cannot be answered without knowing the size of the cube!If the cube were 1 cm on a side the density would be 60.If the cube were 10 cm on a side the density would be 0.06...We cannot determine the answer because we are not given the volume.Density= mass/volumeVolume of a cube=L3 ; where L = side length


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The volume of the cube is (5.0 cm)^3 = 125 cm^3. To find the density, divide the mass by the volume: density = mass / volume = 250 g / 125 cm^3 = 2 g/cm^3. The density of the cube is 2 g/cm^3.

Related Questions

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If a cube is floating and half of it is in the water what is its density?

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