Understanding the Problem
To determine how many cuboids are needed to form a cube, we first need to calculate the volume of both the cuboid and the cube.
Volume of the Cuboid
- The dimensions of the cuboid are 5 cm, 2 cm, and 5 cm.
- Volume of the cuboid = length × width × height
- Volume = 5 cm × 2 cm × 5 cm = 50 cm³
Volume of the Cube
- A cube has all sides equal. To find the side length, we first need to determine the total volume we want to achieve.
- Let’s assume we want a cube with a total volume that is a multiple of the cuboid's volume. The side length of the cube can be calculated from its volume as follows:
- Volume of the cube = side³ (let's denote the side of the cube as 's').
Finding the Side of the Cube
- To find a suitable cube, we can consider various volumes. For example, let’s assume we want a cube with a volume of 1000 cm³.
- We calculate the side length: s = cube root of 1000 = 10 cm.
Calculating the Number of Cuboids
- The volume of the cube is 1000 cm³.
- Number of cuboids required = Volume of the cube / Volume of one cuboid.
- Number of cuboids = 1000 cm³ / 50 cm³ = 20.
Conclusion
To create a cube with a volume of 1000 cm³, Parikshit will need 20 cuboids of dimensions 5 cm × 2 cm × 5 cm.

20 cuboids