Question

If two cubes of volume $216m^3$ are joined end to end to form a cuboid, then 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 $432m^3,360m^2$

As two cubes of volume $216m^3$ are combined to form the cuboid.

$\therefore \text{Volume of cuboid}=216m^3+216m^3=432m^3$
Now,
$\text{Volume of cube}=(side{)}^3$
$\Rightarrow (side{)}^3=216$
$\Rightarrow (side{)}^3=(6{)}^3$
$\Rightarrow Side=6m$


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