Question

3 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

Answer 1

Let the side of a cube be 'a'
Total surface area of cube= 6a²
Total surface area of 3 cubes = 3 *6a² =18a²

After joining 3 cubes in a row,
length of Cuboid =3a
Breadth and height of cuboid = a
Total surface area of cuboid
= 2 ( 3a² + a² + 3a²) = 14 a²

Ratio of total surface area of cuboid to the total surface area of 3 cubes = 14a²: 18a² = 7:9

Answer 2

let the side of cube be Acm
 T.S.A of cube =6a²
                        =3*6A² (∵ 3 cubes are there)
                          18A²

now, 
      length of cuboid=3A
       height &breath of cuboid=A

T.S.A of cuboid=2(lb+bh+lh)
                          =2(3A*A+A*A+3A*A)
                          = 2(3A²+A²+3A²)
                           =6A²+2A²+6A²
                           =14A²

now,
       ratio of T.S.Aof cuboid ÷T.S.A of cubes
          
        =14A²÷18A²
         =7÷9