If each face of the cube is cut by 0.5cm it means that each edge of the cube is now smaller by 1cm (0.5cm from each side). So if original length of cubes edge was `a` then its volume was `a^3`. When woodworker cut the cube its edge is `a-1` and its volume `(a-1)^3`. Since difference between those two volumes is 469 we have equation

`a^3=(a-1)^3+469`

`a^3=a^3-3a^2+3a-1+469`` `

`-3a^2+3a+468=0`

`a^2-a-156=0`

Now we solve this quadratic equation.

`a_(1,2)=(1pm sqrt(1+624))/2`

`a_(1,2)=(1pm25)/2`

`a_1=-12`

`a_2=13`

Since length of cubes edge must be positive `a_1` cannot be edge of the cube.

**So original length of cubes side is 13 and its volume** **is** `13^3=2197.`

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