12. Three cubes of a metal whose edges are in the ratio 3:4:5 are melt

1.	12. Three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted intoa single cube whose diagonal is 12√3 cm. Find the edges of the three cubes.INCERT EXEMPLAR)
Answer» Answer: Let the edges of three cubes be 3X, 4x and 5x respectively. So, the volume of the cube after melting will be = (3x)³ + (4x)³ + (5x)³ = 9x³ + 64x³ + 125x³ = 216x³ Now, let a be the edge of the new cube so formed after melting Then we have, a3 = 216x3 a = 6x We know that, Diagonal of the cube = √(a2 + a2 + a2) = a√3 So, 12√3 = a√3 a = 12 cm x = 12/6 = 2 Thus, the edges of the three cubes are 6 cm, 8 cm and 10 cm respectively.

12. Three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted intoa single cube whose diagonal is 12√3 cm. Find the edges of the three cubes.INCERT EXEMPLAR)

Answer»

Answer: Let the edges of three cubes be 3X, 4x and 5x respectively.

So, the volume of the cube after melting will be = (3x)³ + (4x)³ + (5x)³

= 9x³ + 64x³ + 125x³ = 216x³

Now, let a be the edge of the new cube so formed after melting

Then we have,

a3 = 216x3

a = 6x

We know that,

Diagonal of the cube = √(a2 + a2 + a2) = a√3

So, 12√3 = a√3

a = 12 cm

x = 12/6 = 2

Thus, the edges of the three cubes are 6 cm, 8 cm and 10 cm respectively.