CT 21: Reasoning (Cube and Dice ঘনক এবং পাশা)

1) A cube is divided into 1,000 smaller cubes. If 6 faces of the large cube are painted, how many of the smaller cubes will remain unpainted?

2) A cube has a side length of 4 cm. If it is sliced into 1 cm smaller cubes, how many smaller cubes will have at least one face painted if the original cube was painted on all its faces?

3) A large cube is formed by arranging 64 smaller cubes. If each smaller cube is painted only on its outer surface, how many cubes are painted on exactly two faces?

4) A cube is painted red on all its faces and then divided into 27 equal smaller cubes. How many of these smaller cubes will have exactly two faces painted?

5) A die is rolled, what is the probability of getting a number less than 3?

6) If a cube is painted on two opposite faces and then divided into 64 smaller cubes, how many of these smaller cubes will have paint only on one face?

7) A cube is painted on all six sides and then cut into 64 smaller cubes of equal size. How many of these smaller cubes will have no paint on any side?

8) A standard six-faced die is thrown once. What is the probability that the number obtained is a prime number?

9) A cube is made up of smaller cubes of side 1 cm. If the outermost layer is removed, what will be the volume of the remaining structure if the original cube had a side length of 6 cm?

10) When two dice are thrown simultaneously, what is the probability that the sum of the numbers is greater than 10?