Question

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

Answer 1

first let

three ages are

3x 4x and 5x

volume total=3x^3+4x^3+5x^3=216x^3

now we know after melting volume can not be changed only shape changed

so let new edge = a

new volume=a^3

so equating both volume we get

a^3=216x^3

a=6x

and

as given after melting new dia is

12root3

and

formula of

diagonal is

root 3 a

hence equate it

root 3*a=12 root 3

so

a = 12

put the value of find x

6x=a

so 6x=12

x=2

so old cube ages

3×2,4×2,5×2

6,8,10