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

1.	Three cubes of a metal whose edges are in the ratio 3: 4: 5 are melted and converted into a single cube whose diagonal is 12√3 cm. Find the edges of the three cubes.
Answer» Let the edges of three cubes (in cm) 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.

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

Answer»

Let the edges of three cubes (in cm) 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.