Answer:
The number of cuboids that will be needed to form a cube is 2625 cuboids
Step-by-step explanation:
To form a cube, we have;
The length = The height = The depth
The dimensions of the given cuboid = Length = 75 cm, the width = 35 cm, the depth = 21 cm.
Therefore;
The lowest common multiple of 75, 35, and 21, for the cuboid is given as follows;
75 = 5 × 5 × 3
35 = 5 × 7
21 = 3 × 7
Therefore, multiplying 75 by 7, we get;
75 × 7 = 525
Since 7, 5 and 3 are factors of 525, 35 and 21, can also be factors as we check;
525/35 = 15
525/21 = 25
Therefore, the cube will be;
The length of the cube will consist of 7 pieces of the cuboid, arranged with the side 75 cm facing the front
The depth of the cuboid will be 15 cuboids with the side 35 cm facing the sides
The height of the cuboid will be 25 cuboids with the side 21 cm high
The total number of cuboids is therefore;
7 × 15 × 25 = 2625 cuboids
The number of cuboids that will be needed to form a cube = 2625 cuboids.
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