ravi made a cuboid of plasticine of dimensions 15cm,9cm and 4cm.how many minimum number of such cuboid will be needed to form a cube
Answers
Step-by-step explanation:
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
Answer.
So, Ravi will need 48 cubes to form a cube.
Answer:
side of cube =12cm, Cuboid dimensions 12cm,8cm,3cm
⇒ Volume of cube =(side)
3
=(12)
3
=1728cm
3
Volume of cuboid =12×8×3=288cm
3
No. of cuboids needed to form such cubes =
volume of cuboid
volume of cube
=
288
1728
=6
Hence, 6 cuboids will be needed to form a cube of 12cm.