Question

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?

Answer 1

Solution :-

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 2

Answer:

Solution :-

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.

I hope this answer may helped you.

Step-by-step explanation: