Why does changing the shape of an object have no effect on the density of that object?

Because it's still the same item all you did is change how it looks. The mass and matter stays in the object.
Is this correct

density = mass / volume

if you don't change the amount or add weight, then it has no affect on the density.

Yes, that is correct. Changing the shape of an object does not have an effect on its density because density is defined as the mass of an object divided by its volume. Changing the shape of an object does not alter the amount of matter or mass in the object, only the way it is distributed. Therefore, the mass and volume remain the same, resulting in the same density.

Yes, that is correct. Changing the shape of an object does not have any effect on its density because density is a property of matter and is defined as the mass of an object divided by its volume. When you change the shape of an object, you are simply rearranging the same amount of matter within a different spatial arrangement. The mass of the object remains the same because the amount of matter it contains does not change. Similarly, the volume of the object is also the same because it is determined by the amount of space occupied by the object, regardless of its shape. Therefore, the density, which is the mass divided by the volume, remains constant regardless of the object's shape.