Parikshit makes a cuboid of plastic of sides 5cm, 2cm, 5cm. How many such cuboids will be needed to form a cube?

• A. 30
• B. 15
• C. 20
• D. 25

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 formula for the volume of a cuboid is:

Volume = Length × Width × Height

For Parikshit's cuboid:

• Length = 5 cm
• Width = 2 cm
• Height = 5 cm

Calculating the volume:

Volume = 5 cm × 2 cm × 5 cm = 50 cm³

Volume of the Cube

Next, we need to find the volume of a cube that can be formed using these cuboids. The side length of the cube must be a multiple of the dimensions of the cuboid. The smallest cube that can be formed using the dimensions of the cuboid is:

Side length = 5 cm

Now, we calculate the volume of the cube:

Volume = Side³ = 5 cm × 5 cm × 5 cm = 125 cm³

Calculating the Number of Cuboids

To find out how many cuboids are needed to fill the cube, we divide the volume of the cube by the volume of one cuboid:

Number of cuboids = Volume of Cube / Volume of Cuboid

Number of cuboids = 125 cm³ / 50 cm³ = 2.5

Since we cannot have a fraction of a cuboid, we need to find the smallest whole number that can fill the cube completely. Therefore, we need:

Number of cuboids = 3

Final Answer

Thus, the answer is not listed in the options provided. However, if we consider the total volume needed to fill a larger cube, we would need:

• A total of 30 cuboids to fill a cube of side 10 cm (since 10 cm³ = 1000 cm³).

So, the closest answer based on the options given would be A. 30.