Question:
Two cubes each of volume 125 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.
Solution:
Let the edge of the cube be $a$.
As,
Volume of the cube $=125 \mathrm{~cm}^{3}$
$\Rightarrow a^{3}=125$
$\Rightarrow a=\sqrt[3]{125}$
$\Rightarrow a=5 \mathrm{~cm}$
So,
Length of the resulting cuboid, $l=2 \times 5=10 \mathrm{~cm}$,
Breadth of the resulting cuboid, $b=5 \mathrm{~cm}$ and
Height of the resulting cuboid, $h=5 \mathrm{~cm}$
Now,
Surface area of the resulting cuboid $=2(l b+b h+h l)$
$=2 \times(10 \times 5+5 \times 5+5 \times 10)$
$=2 \times(50+25+50)$
$=2 \times 125$
$=250 \mathrm{~cm}^{2}$
So, the surface area of the resulting cuboid is 250 cm2.