Question

Paras makes a cuboid of plasticine of sides 21cm 18 cm 14 centimetre how many such cuboids will be needed to form a cube???

Answer 1

Answer:

$\sf{\underline{LCM \:of\: 21, 18, 14}}$ = 126

Thus, each side of the cube will be = 126 cm

Number of cuboids = Volume of cube/Volume of cuboid

=》 Number = $\tt{\frac{126 \times126 \times126}{21 \times18 \times14}}$

=》 Number = 378

Answer 2

Solution :-

The volume of the cuboid = 21 cm × 18 cm × 14 cm

= 5292 cm^3

The cube is formed by stacking many such cuboids and it will have side lengths which are multiple of 21, 18 and 14

The smallest such cube will have a side length of LCM of 21, 18 and 14

LCM of 21, 18 and 14 -

21= 3*7

18 = 2*3*3

14 = 2*7

LCM = 2*3*3*7= 126

The smallest such cube will have side length of 126cm and volume of (126*126*126) cm^3

Number of cuboids of volume (21*18*14) cm^3 that will fit into a cube of volume (126*126*126) cm^3

= (126*126*126)/(21*18*14)

= 2000376/ 5292

= 378 cuboids

Answer.

So, paras will need 378 cuboids to form a cube.