Anita has a cuboid of length 5 cm, width 4 cm and height 4 cm. How many such cuboids will she need to make the smallest possible cube ?

Given :

Cuboid of sides 5 cm , 4 cm , 4 cm.

To do :

We have to find how many such cuboids require to make a smallest possible cube.

Solution :

Volume of a cuboid of height h, length l and breadth is lbh.

This implies,

Volume of the given cuboid $= 5 cm \times 4 cm \times 4 cm = 20 \times 4 cm^3 = 80 cm^3 $

The minimum length required to form a cube = LCM of 5,4 and 4 $= 5\times 4 = 20$.

Therefore,

Minimum length required to form a cube $= 20 cm$.

Volume of the cube so formed $= (20 cm)^3 = 8000 cm^3$ .

Number of such cuboids required $= \frac {8000}{80}  = 100$.

Number of cuboids required to make a smallest possible cube is 100

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Updated on: 10-Oct-2022

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