Ravi made a cuboid of plasticine of dimensions 12cm,8cm and 3cm.How many minimum number of such cuboids will be needed to form a cube?
Answers
Answer:
The volume of the cuboid = 12 cm × 8 cm × 3 cm
= 288 cu cm
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 -
12 = 2*2*3
8 = 2*2*2
3 = 3
LCM = 2*2*2*3 = 24
The smallest such cube will have side length of 24 and volume (in cu cm) of (24*24*24) cu cm.
Number of cuboids of volume (12*8*3) cu cm that will fit into a cube of volume (24*24*24) cu cm.
= (24*24*24)/(12*8*3)
= 13824/288
= 48 cuboids
Solution:
- Ravi made a cuboid of plasticine .
- Dimensions of cuboid are 12cm, 8cm and 3 cm
Therefore,
- The length of the cuboid = 12 cm
- The Breath of the cuboid = 8cm
- The height of the cuboid = 3 cm
As we know that,
The volume of cuboid = L * B * H
Pur the required values,
Volume of cuboid = 12 * 8 * 3
Volume of cuboid = 96 * 3
Volume of cuboid = 288cm^3
Now,
We have to find the number of such cuboids that is needed to form a cube of edge 12 cm . So for that we have to find the volume of cube
As we know that,
Volume of cube = a^3
Volume of cube = 12 * 12 * 12
Volume of cube = 144 * 12
Volume of cube = 1728cm^2
Now,
- Let the number of cuboids be x
Therefore,
No. of cuboids = Volume of cube / Volume of cuboid.
x = 1728 / 288
x = 6
Hence, The number of cuboids needed to make a cube of 12 cm is 6 cuboids..