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MCQ

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

#### Options

7 : 9

49 : 81

9 : 7

27 : 23

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#### Solution

Let, a → Side of each cube

So, the dimensions of the resulting cuboid are,

Length(l) = 3a

Breadth (b) = a

Height (h) = a

Total surface area of the cuboid,

=2(lb + bh + hl)

=2[(3a) a + a × a + a (3a)]

= 14 a^{2}

Sum of the surface areas of the three cubes,

= 3 (6a^{2})

= 18 a^{2} Required ratio,

=`(14a^2)/(18a^2)`

=7:9

Thus, the required ratio is 7: 9 .

Concept: Surface Area of a Cuboid

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