Question

Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid is $648$ $c{m}^2$; find the length of edge of each cube.

• A. $4$ cm
• B. $9$ cm
• C. $5$ cm
• D.
  $6$ cm

Answer 1

The correct option is D

$6$ cm
Given, four identical cubes are joined end to end to form a cuboid.

Let the side of cube be $a$, then length of cuboid thus formed be $4a$, breadth be $a$, height be $a$.

Surface area of resulting cuboid be $648$ ${cm}^2$.
Total surface area of resulting cuboid $=2(lb+bh+lh)$
$\Rightarrow 648=2(4a\times a+a\times a+4a\times a)\Rightarrow 648=2\left(9a^2\right)\Rightarrow 648=18a^2\Rightarrow a^2=36\Rightarrow a=6$ cm
Length of edge of cube $=6$ cm