Q2 of 76 Page 18

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.

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


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