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