Question

A hollow square-shaped tube open at both ends is made of iron. The side of internal square is $5$ cm and the length of the tube is $8$ cm. There is $192$ $c{m}^3$ of iron in this tube. Find its thickness.

Answer 1

Let us take thickness of the tube $=x$ cm
Side of the external square $=(5+2x)$ cm
External volume of the tube $-$ its internal volume $=$ volume of iron in the tube
$\Rightarrow \{(5+2x)\times (5+2x)\times 8\}-5\times 5\times 8=192$
$\Rightarrow 8\left\{\right({5+2x)}^2-25\}=192$
$\Rightarrow {(5+2x)}^2=49$
$\Rightarrow 5+2x=7$
$\Rightarrow x=1$
Therefore, thickness is $1$ cm.