Question

Three cubes of sides $4cm$ each are joined end to end to from a cuboid. What is the ratio of the surface area of the resulting cuboid to the total surface area of the three cubes?

• A. $4:9$
  
• B. $1:3$
  
• C. $5:3$
  
• D. $7:9$
  

Answer 1

The correct option is D $7:9$

The dimensions of the resulting cuboid are:
length $=12cm$, breadth $=4cm$, height $=4cm$
$\therefore$ Surface area of the cuboid $=2(12\times 4+4\times 4+12\times 4)c{m}^2$
$=2\times 112c{m}^2=224{}^2$
Surface area of the three cubes $=3\times 6\times {\left(4\right)}^{2}c{m}^2=288c{m}^2$
$\therefore$ Required ratio $=224:288=7:9$