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Q.

Three equal cubes are placed adjacently in a row. The ratio of total surface area on the new cuboid to that of the sum of the surface areas of the three cubes is[[1]].


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Detailed Solution

Three equal cubes are placed adjacently in a row. The ratio of total surface area on the new cuboid to that of the sum of the surface areas of the three cubes is 7:9.
The total surface area of the cube =6 a 2 .
Total surface area of 3 cubes is
= 3 × 6a²
= 18a²   When 3 cubes are placed adjacent to each other, dimensions of the resultant cuboid are length = 3a, breadth = a, height = a.
Total surface area of cuboid =2 lb+bh+lh               Substituting values,
= 2(3a×a+3a×a+a×a)
= 2 3 a 2 +3 a 2 + a 2 = 2 7 a 2 = 14a2 The ratio of surface area of cuboid and surface area of cube will be,    Question ImageRatio = 7:9.
Therefore, the final answer is 7:9.
 
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