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Hello everyone. I'm currently working on a project (independent study and not homework) and I find myself having to calculate the volume of a cube with rounded corners and I'm stumped. Any help would be really appreciated.

The cube itself is 8 cubic meters (2m on each side) and the rounded corners are 406mm from what would otherwise be a corner point to the end of the curve in all three directions spreading out from the would-be corner point. I need to be fairly precise with this calculation but I'm afraid my mathematics know-how isn't getting me very far. I appreciate the fact that this a learning forum and so I do not expect a direct answer to this but if somebody would be good enough to provide me with a formula into which I can put these figures I would really be very grateful. I've included an image of my problem in case I'm not being very well understood. Thank you all for reading.

The cube itself is 8 cubic meters (2m on each side) and the rounded corners are 406mm from what would otherwise be a corner point to the end of the curve in all three directions spreading out from the would-be corner point. I need to be fairly precise with this calculation but I'm afraid my mathematics know-how isn't getting me very far. I appreciate the fact that this a learning forum and so I do not expect a direct answer to this but if somebody would be good enough to provide me with a formula into which I can put these figures I would really be very grateful. I've included an image of my problem in case I'm not being very well understood. Thank you all for reading.

**1. Find the volume of a cube with rounded corners**

Volume of un-rounded cube 2³ = 8 cubic meters.

Length of rounding = 406mmVolume of un-rounded cube 2³ = 8 cubic meters.

Length of rounding = 406mm

**2. Width * Height * Depth ..... after that I just dunno.****3. Completely Stumped.**