Mathematics3 cubes of metal whose sides are in ratio 3:4:5 are melted and converted into a single cube whose diagonal is 18√3 cm. The sides of cubes are ____, ____, ____.

3 cubes of metal whose sides are in ratio 3:4:5 are melted and converted into a single cube whose diagonal is 18√3 cm. The sides of cubes are ____, ____, ____.


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    Solution:

    Let the sides of the cubes be 3x, 4x and 5x.
    Let the sides of the single cube be a.
    As,
    Diagonal of the single cube = 183 cm
    a3 = 183 a = 18 cm
    Now,
    Volume of the single cube = Sum of the volumes of the metallic cubes
    a3 = (3x)3 +  (4x)3+  (5x)3
    183 = 27x3 +  64x3+  125x3
    183 = 216x3 6x = 18
    x = 3
    So, the Sides of the cubes are 3 x 3= 9 cm, 4 x 3 = 12 cm and 5 x 3 = 15 cm.
    Hence, the Sides of the given cubes are 9 cm, 12 cm and 15 cm.
     
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