Biology, asked by ashishnarigara5250, 11 months ago

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

Answered by tejaswinimogal11
5

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

Answered by Anonymous
4

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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..

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