Question

Three equal cubes are placed in a row touching each other Find the ratio of the total surface area of the resulting cuboid to that of the sum of surface areas of the three cubes

• A. 5 : 7
• B. 7 : 9
• C. 9 : 7
• D. None of these

Answer 1

Answer: (B)

7 : 9

surface area of 1 cube=$6\ast a^2$ (a=edge)
surface areas of 3 cube= $3\ast 6\ast a^2=18a^2$
If Three equal cubes are placed in a row touching each other, then total surface area of the resulting cuboid=$5a^2+4a^2+5a^2=14a^2$
ratio of the total surface area of the resulting cuboid to that of the sum of surface areas of the three cubes=
$R=\frac{14a^2}{18a^2}$
$R=\frac{7}{9}$
Answer (B) 7:9