Question

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

Answer 1

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 a²

Sum of the surface areas of the three cubes,

= 3 (6a²) 

= 18 a²                                                                            Required ratio,

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

=7:9

Thus, the required ratio is 7: 9 .