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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 l b + b h + l h

Substituting values,
=

2 (3 a × a + 3 a × 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 Image

Question Image

Ratio = 7:9.
Therefore, the final answer is 7:9.

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