Question

Three cubes of metal whose edges are in the ratio 3:4:5 are melted and converted into a single cube whose diagonal is 12root3 .Find the edges of three cubes

Answer 1

Let the edges of the three cubes = 3x, 4x and 5x
Then,Their volume
27x^3,64x^3,125x^3

Given : The length of the diagonal of the single cube = 12√3
As we know that,the length of the diagonal of a cube of side a=a√3
⇒ edge of the single cube = 12 cmNow, 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
27x^3+64x^3+125x^3=1728
216x^3=1728
x^3=8
x=2
∴ The edges of the three cubes are 6cm, 8cmand 10 cm