Question

Three cubes of a metal whose edges are in the ratio 3 : 4 : 5 are melted and converted into a single cube of diagonal 24 3 cm. find the edges of the three cubes.

Answer 1

let the edge of the cubes be- 3x, 4x and 5x.
∴ volume= (3x)³, (4x)³ and (5x)³
 = 27x³ , 64x³ and 125x³
given length of diagonal is 24√3 cm 
we know that length of the diagonal of a cube of side 
a= a√3
⇒ edge of single cube = 12cm
new volume of single cube - 1728 cm³
since the three cubes are melted and recast into 1 cube,
 volume of 3 cube = vol of new cube.
⇒27x³ +64x³ +125x³ = 1728 cm³
⇒ 216x³ = 1728 cm³
⇒ x³ =1728/216
⇒ x³ = 8
⇒ x=2
∴ edges are 6 cm , 8cm and 15cm