Question

the edge of three metallic cube are in the ratio of 3:4:5 these cubes are recasted into a single cube whose diagonal is 12 root 3cm find the edge of three cubes

Answer 1

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.
                   

Answer 2

Answer:

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.