Question

Two cubes of volume $216m^3$ are joined end to end to form a cuboid. Find the volume and total surface area of the cuboid.

• A. $432m^3,380m^2$
• B. $216m^3,160m^2$
• C. $432m^3,360m^2$
• D. $430m^3,180m^2$

Answer 1

The correct option is C

$432m^3,360m^2$

Two cubes of volume $216m^3$ are combined to form the cuboid.
Therefore, volume of cuboid $=216m^3+216m^3=432m^3$
Now,
$Volumeofcube=\left(side{)}^3\right(side{)}^3=216(side{)}^3=(6{)}^{3}Side=6$

The formed cuboid has dimension $12m\times 6m\times 6m$
So, the total surface area of cuboid = 2(lb + bh + hl)
Total surface area of cuboid $=2\left(\right(12\times 6)+(6\times 6)+(6\times 12\left)\right)$
$\Rightarrow$ Total surface area of cuboid = 360 $m^2$