MathematicsThree equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the resulting cuboid to that of the sum of the total surface areas of the three cubes.

Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the resulting cuboid to that of the sum of the total surface areas of the three cubes.


  1. A
     7:9
  2. B
     2:3
  3. C
     4:9
  4. D
     7:5 

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    Solution:

    Total cubes= 3.
    Suppose edge of each cube = x
    Thus, one cube surface area
    = 6x2
    Three cubes surface area
    = 3×6x2=18x2
    When cubes kept in a row,
    Length (l) = 3x
    Breadth (b) = x
    Height (h) = x
    Now, surface area of this cuboid,
    = 2l×b+b×h+h×l
    = 23x×x+x×x+x×3x
    = 23x2+x2+3x2
    =2×7x2
    =14x2     
    Ratio of both cubes,
    = 14x2:18x2 
    = 7:9
    Option 1 is Correct.
     
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