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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 12√3 cm. Find the edges of the three cubes.

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In this question we have to find edges of the three cubes having cubes of a metal whose edges are in the ratio 3: 4: 5 are melted and converted into a single cube whose diagonal is 12√3 cm.

This question is from r d sharma class 10 maths.

I found this question while doing maths class 10. I need help in getting the solution.

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1 Answer

  1. Let the edges of three cubes (in cm) be 3x, 4x and 5x respectively.

    So, the volume of the cube after melting will be = (3x)3 + (4x)3 + (5x)3

    = 9×3 + 64×3 + 125×3 = 216×3

    Now, let a be the edge of the new cube so formed after melting

    Then we have,

    a3 = 216×3

    a = 6x

    We know that,

    Diagonal of the cube = √(a2 + a2 + a2) = a√3

    So, 12√3 = a√3

    a = 12 cm

    x = 12/6 = 2

    Thus, the edges of the three cubes are 6 cm, 8 cm and 10 cm respectively.

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