Question

Three cubes of the 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 1

Here is the answer to your query

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

Then their volume

Given : The length of the diagonal of the single cube =

We know that the length of the diagonal of a cube of side

⇒ edge of the single cube = 12 cm

Now, volume of the single cube = (12 cm)3 = 1728, cm3

Since the three cubes are melted and converted into single cube

⇒ Sum of volumes of three cubes = volume of single cube

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

Answer 2

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.