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

Question

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

Philoid · Accepted Answer

Given,

Ratio of edge of 3 cubes = 3:4:5

Diagonal of new cube formed = 12√3 cm

Let edges are = 3x ,4x 5x

Comined volume =

= 216 x³

New diagonal = √3a = 12√3 = a = 12 cm

So, a³ = 216 x³

= 12×12×12 = 216 x³

=

=x =

So , edges are = 3x = 3×2 = 6 cm

=4x = 4×2 = 8cm

= 5x = 5×2 = 10 cm