The volume of the cube would be 12x12x12 = 1728
Now we have to calculate the volume of the inverted pyramyd and substract it from the volume of the cube
If we see the top of the cube, this is how it looks (sse the image below), so each sdie of the base of the pyramid can be calculated by pythagoras:
Side of the pyramid = sqrt(6^2 + 6^2) = sqrt(36 + 36) = sqrt(72) = 8.48528
The height of the pyramid is 12
Volume of a squared pyramid = (1/3) x area of the base x height = (1/3)(8.48528)^2 x 12 = (1/3)(72)(12) = 288
Volume of the composite solid = 1728 - 288 = 1440
Answer:
1440 cubic inches