Calculating the Volume of the Cuboid:
To find out how many cuboids will be needed to form a cube, we first need to calculate the volume of the plasticine cuboid that Sonu has made. The formula to calculate the volume of a cuboid is:
Volume = length x width x height
Given that the sides of the plasticine cuboid are 7 cm, 3 cm, and 7 cm, we can substitute these values into the formula:
Volume = 7 cm x 3 cm x 7 cm
Volume = 147 cm³

Calculating the Volume of a Cube:
To form a cube using the plasticine cuboids, we need to calculate the volume of a cube. The formula to calculate the volume of a cube is:
Volume = side³
Since all sides of a cube are equal, we can take any side length. Let's take the side length to be 7 cm (the length of one of the sides of the plasticine cuboid):
Volume = 7 cm x 7 cm x 7 cm
Volume = 343 cm³

Determining the Number of Cuboids Needed:
Now, we need to find out how many plasticine cuboids are required to form a cube with a volume of 343 cm³. We can divide the volume of the cube by the volume of one cuboid to get the number of cuboids needed:
Number of cuboids = Volume of cube / Volume of one cuboid
Number of cuboids = 343 cm³ / 147 cm³
Number of cuboids ≈ 2.33
Since we cannot have a fraction of a cuboid, we need to round up to the nearest whole number. Therefore, we would need 3 plasticine cuboids to form a cube with the given dimensions.
In conclusion, Sonu would need 3 cuboids of plasticine to form a cube using cuboids with sides of 7 cm, 3 cm, and 7 cm.