- #1

Will_H

- 3

- 0

A 1" cube has three holes drilled in it, each hole connecting the centres of opposite faces, thus forming a cavity in the centre joined to the surface by six holes. The holes have diameter 1/2". What is the volume of the remaining material?

I have calculated the solution for two holes; the object shared by by each of the two holes is one twelth of a cubic inch (found by integrating for the volume of the central shape, a stack of squares with sides that varying as the cord of a circle).

I struggled to find the solution for three holes. I have found that the shape in the centre is called a Steinmetz Solid and has volume (16-sqrt(128))*r^3.

Using this I have calculated the final volume of the holey cube to be 0.567608 cubic inches, while a 3DCAD model has been constructed and the volume is 0.58773.

Does anyone know the answer, have a solution or have any help?

Thanks...