UPSC CDS 2 2021 Math Paper

Given, volume of one cube =343cm3
Let the length of the side of the cube be a unit.When cubes are joined end to end, length of the resulting cuboid will be 3a but breadth and height will be the same.
In cuboid, I=3a,b=a and h=a
Total surface area of cuboid =2(lb+bh+hl)
=2(3a×a+a×a+a×3a)
=2(3a2+a2+3a2)
=2(7a2)=14a2 ... (i)
Since, cuboid is formed using 3 cubes.
Therefore, volume will remain same.
∴V‌cuboid ‌=3×V‌Cube ‌
⇒1×b×h=3×343
⇒3a×a×a=3×343
⇒a3=343⇒a=7cm
Putting, a=7cm into Eq. (i), we get
Total surface area of cuboid
=14×(7)2=686cm2