Answer: The volume of cheese remaining is 7 cubic inches (7 in³)
Step-by-step explanation: The cheese is in the shape of a cylinder. The volume of a cylinder is given as follows;
Volume = πr²h
Where r = radius of the top of the cylinder and h = the height of the cylinder.
In this case, the cheese has its radius as 3 inches (that is diameter divided by 2). Also the height is given as the thickness of the cheese which is 2 inches. Note also that part of the cylindrical cheese has been eaten leaving only a potion which has an angle of 45 degrees.
The volume of the left over portion therefore can be calculated as follows;
Volume = (∅/360) x πr²h
Volume = (45/360) x 3.14 x 3² x 2
Volume = (1/8) x 3.14 x 9 x 2
Volume = (1/8) x 56.52
Volume = 7.065
Volume ≈ 7
Therefore the volume of cheese that remains is 7 cubic inches (7 inches³) approximately.