Introduction

To determine how many cuboids of plasticine with given dimensions are needed to form a cube, we need to analyze the relationship between the dimensions of a cuboid and a cube.

Understanding the Problem

Parikishit has made a cuboid of plasticine with sides measuring 5cm, 2cm, and 5cm. Now, we need to find out how many such cuboids are required to form a cube.

Analysis

To form a cube, all sides of the cuboid must be equal in length. In this case, two sides of the cuboid are 5cm long, while the remaining side is 2cm long. Therefore, we need to determine the dimensions of a cube that can accommodate these cuboids.

Determining the Side Length of the Cube

Since a cube has all sides equal in length, we need to find a common length that can accommodate both the 5cm and 2cm sides of the cuboid.

- The greatest common divisor (GCD) of 5cm and 2cm is 1cm.
- Dividing both the lengths by the GCD, we get 5cm ÷ 1cm = 5 and 2cm ÷ 1cm = 2.
- Therefore, the dimensions of the cube will be 5cm × 5cm × 2cm.

Calculating the Volume of the Cube and Cuboid

To determine how many cuboids are needed to form a cube, we need to compare their volumes.

- The volume of the cube is calculated by multiplying the length, width, and height: 5cm × 5cm × 2cm = 50cm³.
- The volume of the cuboid is calculated similarly: 5cm × 2cm × 5cm = 50cm³.

Determining the Number of Cuboids Required

To find the number of cuboids required to form a cube, we need to divide the volume of the cube by the volume of the cuboid.

- Number of cuboids required = Volume of the cube / Volume of the cuboid = 50cm³ / 50cm³ = 1.

Conclusion

Parikishit will need one more cuboid of plasticine with the given dimensions (5cm, 2cm, 5cm) to form a cube. The side length of the cube will be 5cm × 5cm × 2cm.

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