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

Options

A. `7:9`
B. `7:3`
C. `5:9`
D. `1:9`

Answer

A

Explanation

Let the side of a metal cube = `x`
`therefore` Surface area of one cube `= 6x^(2)`
`rArr` Surface area of three cubes `= 18x^(2)`
When three cubes are placed adjacently in a row they a cuboid in which `l = 3x, b = x` and `h = x`

`therefore` Its surface area `=2(3x xx x + x xx x + x xx 3x) = 14x^(2)`
Now, ratio of total surfacearea of resulting cuboid to sum of total surface area of resulting cuboid to sum of total surface areas of three cubes
`=(14 x^(2))/(18 x^(2))=(7)/(9)=7 : 9`