Question

Three cubes with sides in the ratio 3:4:5 are melted to form a single cube whose diagonal is 18 3 cm. the sides of the cubes are (in cm)

Answer 1

Ratio of the lengths of the edges of the cubes = 3:4:5 Let the edges of the cubes be 3x, 4x and 5x Volumes of the cubes = (3x)3 cu units, (4x)3 cu units, (5x)3cu units                                 = 27x3 cu units, 64x3 cu units, 125x3 cu units Total volume = (27x3 +  64x3 + 125x3)                    = 216 x3 cu units Diagonal of the new cube formed = 15√3  Let the edge of the new cube formed = 's'  units Diagonal = s√3 ⇒ s√3 = 15√3 ⇒ s = 15 units Volume of the new cube formed = (15)3 cu units = 3375 cu units ⇒ 216 x3 = 3375 ⇒ x3 = (3375 / 216) ⇒ x = 15/6 = 5/2 = 2.5Therefore, the edges of the cubes are (3 x 2.5) i.e. 7.5 units, (4 x 2.5) i.e. 1 units, (5 x 2.5) i.e. 1.25 units.