Number of Cuboids to form a Cube from Plasticine Cuboids

To determine the number of cuboids needed to form a cube, we need to consider the dimensions of the given plasticine cuboids and analyze how they can be arranged to create a perfect cube.

Given Information:
- Dimensions of the plasticine cuboids: 5 cm, 2 cm, and 5 cm

Step 1: Determine the Side Length of the Cube
To form a cube, all the sides must be equal in length. Therefore, we need to find the common side length that can be obtained by combining the given cuboids.

Since the cuboids have dimensions of 5 cm, 2 cm, and 5 cm, we can observe that the longest side is 5 cm. Hence, the common side length of the cube will be 5 cm.

Step 2: Analyze the Arrangement of Cuboids to Create a Cube
To form a cube, we need to align the cuboids in such a way that their sides coincide to create a perfect shape. Let's consider the given cuboids and analyze their arrangement possibilities.

Possible Arrangement:
- Place two cuboids with dimensions 5 cm, 2 cm, and 5 cm side by side, sharing their 5 cm sides. This will create a base with dimensions 5 cm (length) x 4 cm (width) x 5 cm (height).
- On top of this base, place another cuboid with dimensions 5 cm, 2 cm, and 5 cm, aligning its 5 cm side with the height of the base. This will create a structure with dimensions 5 cm (length) x 4 cm (width) x 10 cm (height).

Step 3: Calculate the Number of Cuboids Needed
To form a cube, we need to ensure that all sides have the same length. In the given arrangement, the length and width of the structure are 5 cm and 4 cm, respectively. To make the length and width equal, we need to stack two such structures side by side.

Hence, we can conclude that a total of 2 cuboids with dimensions 5 cm, 2 cm, and 5 cm are needed to form a cube.

Summary:
To form a cube using plasticine cuboids with dimensions 5 cm, 2 cm, and 5 cm, we need to stack two cuboids side by side to create a structure with dimensions 5 cm (length) x 4 cm (width) x 10 cm (height). By repeating this arrangement, a cube can be formed using a total of 2 cuboids.

Volume of 1 cuboid = 5×5×2 cm^3 = 50 cm^3
To make a cube from the cuboid we need prime factors in the form of triplets but here 5 and 2 are not in the form of triplet, so we need
one 5 and two 2's = 5×2×2
50×5×2×2 = 5×5×2×5×2×2
1000 = 5^3 × 2^3
Hence, we need 20 cuboid to form a cube