Sonam makes a cuboid of plasticine of dimensions 12 cm by 8 cm by 3 cm. What minimum number of such cuboids will she need to form a cube?
Answers
The volume of the cuboid = 12 cm × 8 cm × 3 cm = 288 cm cube
The cube is formed by stacking many such cuboids and it will have side lengths which are multiple of 12, 8 and 3.
The smallest such cube will have a side length of LCM of 12, 8 and 3.
LCM of 12, 8 and 3 = 24
The smallest such cube will have side length of 24 and volume of (24*24*24) cm cube.
Number of cuboids of volume (12*8*3) cm cube that will fit into a cube of volume (24*24*24) cm cube = (24*24*24)/(12*8*3)
= 13824/288
= 48 cuboids
So, Sonam will need 48 cubes to form a cube.
Answer:
The volume of the cuboid = 12 cm × 8 cm × 3 cm = 288 cm cube
The cube is formed by stacking many such cuboids and it will have side lengths which are multiple of 12, 8 and 3.
The smallest such cube will have a side length of LCM of 12, 8 and 3.
LCM of 12, 8 and 3 = 24
The smallest such cube will have side length of 24 and volume of (24*24*24) cm cube.
Number of cuboids of volume (12*8*3) cm cube that will fit into a cube of volume (24*24*24) cm cube = (24*24*24)/(12*8*3)
= 13824/288
= 48 cuboids
So, Sonam will need 48 cubes to form a cube.
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