To form a cube from cuboids of plasticine, the length, width, and height of the cube must all be the same. Therefore, the length of each edge of the cube will be the same as the length of the side of each cuboid.
The dimensions of the cuboid are 3 cm x 4 cm x 5 cm. The greatest common factor of these three dimensions is 1 cm. This means that the cuboid cannot be divided into smaller pieces with integer side lengths that could be reassembled to form a cube.
To form a cube with edge length x, the number of cuboids required in each dimension is x/3, x/4, and x/5, respectively. To ensure that the dimensions of the cube are integers, x must be a multiple of both 3 and 4 and 5, which means it must be a multiple of the least common multiple (LCM) of 3, 4, and 5. The LCM of 3, 4, and 5 is 60.
Thus, the length of each edge of the cube must be 60 cm, and the number of cuboids required in each dimension is 60/3 = 20, 60/4 = 15, and 60/5 = 12, respectively.
Therefore, the total number of cuboids required to form the cube is 20 x 15 x 12 = 3600. David will need 3600 cuboids of plasticine to form a cube.
Answers & Comments
Answer:
Given numbers
=
5
×
2
×
5
Since, Factors of 5 and 2 both are not in group of three.
Therefore, the number must be multiplied by
2
×
2
×
5
=
20
to make it a perfect cube. Hence he needs 20 cuboids.
Step-by-step explanation:
To form a cube from cuboids of plasticine, the length, width, and height of the cube must all be the same. Therefore, the length of each edge of the cube will be the same as the length of the side of each cuboid.
The dimensions of the cuboid are 3 cm x 4 cm x 5 cm. The greatest common factor of these three dimensions is 1 cm. This means that the cuboid cannot be divided into smaller pieces with integer side lengths that could be reassembled to form a cube.
To form a cube with edge length x, the number of cuboids required in each dimension is x/3, x/4, and x/5, respectively. To ensure that the dimensions of the cube are integers, x must be a multiple of both 3 and 4 and 5, which means it must be a multiple of the least common multiple (LCM) of 3, 4, and 5. The LCM of 3, 4, and 5 is 60.
Thus, the length of each edge of the cube must be 60 cm, and the number of cuboids required in each dimension is 60/3 = 20, 60/4 = 15, and 60/5 = 12, respectively.
Therefore, the total number of cuboids required to form the cube is 20 x 15 x 12 = 3600. David will need 3600 cuboids of plasticine to form a cube.