A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct? I. The minimum number of cuts is 9. II. The number of smaller pieces which are not painted on any face is 6. Select the correct answer using the code given below:

To solve this problem, we need to understand how cuts in a cube relate to the number of pieces formed.

Statement I: The minimum number of cuts. To get 60 pieces with the minimum number of cuts, we divide the cuts among the three axes (x, y, and z) as evenly as possible. Let the number of pieces along the axes be a, b, and c. Then a times b times c equals 60. The number of cuts is (a-1) plus (b-1) plus (c-1). To minimize cuts, a, b, and c should be close to each other. For 60, the best combination is 3, 4, and 5. The cuts would be (3-1) + (4-1) + (5-1) which equals 2 + 3 + 4 = 9. Thus, Statement I is correct.

Statement II: Number of unpainted pieces. The pieces with no paint are those located in the inner core of the cube. If the cube is divided into a, b, and c pieces along the axes, the inner pieces are found by subtracting 2 from each dimension (to remove the painted outer layers). So, the unpainted pieces are (a-2) times (b-2) times (c-2). Using our dimensions 3, 4, and 5, we get (3-2) times (4-2) times (5-2), which is 1 times 2 times 3 = 6. Thus, Statement II is also correct.

Since both statements are correct, the correct answer is C.