Question

Two identical cubes each of volume $216c{m}^3$ are joined together end to end. What is the surface area of the resulting cuboid?

Answer 1

Let the length of a side of a cube = a cm

Given , volume of the cube , $a^3=216c{m}^3\Rightarrow a=6cm$
On joining two cubes, we get a cuboid whose
Length , l = 2a cm
Breadth , b = a cm
And height , h = a cm
Now, surface area of the resulting cuboid = 2 (lb+bh+lh)
=2(2a.a+a.a+a.2a)
$=2(2a^2+a^2+2a^2)=2\left(5a^2\right)$
$=10a^2=10(6{)}^2=360c{m}^2$­