Question

Five equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the cuboid to the sum of the total surface area of the five cubes.

• A. 8 : 15
• B. 10 : 11
• C. 12 : 13
• D. 11 : 15

Answer 1

The correct option is D 11 : 15

Let the cubes have a side length of $a$.
Then, TSA of a cube $=6(side{)}^2=6a^2$
$\Rightarrow$ TSA of five such cubes $=30a^2$

Also, the length, breadth, and height of the new cuboid formed by placing these five cubes adjacently in a row are 5a, a, and a respectively.
$\Rightarrow$ TSA of a cuboid $=2(lb+bh+hl)$
$\Rightarrow$ TSA of the given cuboid $=2(5a^2+a^2+5a^2)=22a^2$

Thus, the required ratio is $22a^2:30a^2=11:15.$