three metal cubes whose edge measure 3cm, 4cm and 5cm respectively are melted to form a single cube, find its edge and its diagonal ​​

Ratio of the lengths of the edges of the cubes = 3:4:5
Let the edges of the cubes be 3x, 4x and 5x
Volumes of the cubes = (3x)3 cu units, (4x)3 cu units, (5x)3 cu units
                                = 27x3 cu units, 64x3 cu units, 125x3 cu units
Total volume = (27x3 +  64x3 + 125x3)
                   = 216 x3 cu units
Diagonal of the new cube formed = 15√3 
Let the edge of the new cube formed = 's'  units
Diagonal = s√3 
⇒ s√3 = 15√3
⇒ s = 15 units
Volume of the new cube formed = (15)3 cu units = 3375 cu units
⇒ 216 x3 = 3375
⇒ x3 = (3375 / 216)
⇒ x = 15/6 = 5/2 = 2.5
Therefore, the edges of the cubes are (3 x 2.5) i.e. 7.5 units, (4 x 2.5) i.e. 1 units, (5 x 2.5) i.e. 1.25 units.

thanks a lottttt chandana for answering

3³+4³+5³=216      216=a³  or. 6³ = a³     Or  a=6.       Diagonal. =.  under root ( 3a )   Or diagonal = under root (18) or.  3 underoot ( 2. )

3³ +4³ +5³ =216  216=a³ or. 6 = a Diagonal. =. under root ( 3a )  Or diagonal = under root (18)  or. 3 underoot ( 2. )