MathematicsThree 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  . Find the edges of the three cubes.

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  . Find the edges of the three cubes.


  1. A
    6 units, 7 units and 8 units
  2. B
    6 units, 8 units and 10 units
  3. C
    5 units, 7 units and 9 units
  4. D
    5 units, 6 units and 7 units 

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    Solution:

    Given that 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  .
    Let the three cubes of metals be 3x, 4x and 5x.
    Volume of cube = (side)3
    Now, according to the problem, this cubes are melted to form a single cube.
    Then the volume of new cube = (33+43+53)x3.
    ⇒ Volume = (27+64+125)x3
    ⇒ Volume = 216x3
    ⇒ Volume = (6x)3
    Then the side of the new cube is 6x.
    The diagonal of a cube is given by a 3   where a is the side of the cube.
    We get,
    6x 3 =12 3     a=6x x=2   Thus, the edges of the cubes are,
    3x = 6 units
    4x = 8 units
    5x = 10 units
    Hence, the edges of the cubes are 6 units, 8 units and 10 units.
    Therefore, the correct answer is option (2).
     
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