Question

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

• A. $192$cm
• B. $182$cm
• C. $105$cm
• D. None of the above

Answer 1

Answer: (D)

None of the above

Let us take the thickness of the tube $=x$ cm
Side of the external square $=(5+2x)$ cm
Ext. vol. of the tube- its internal vol.= vol. of iron in the tube

$\{(5+2x)\times (5+2x)\times 8\}-5\times 5\times 8=192$

$8\left\{\right({5+2x)}^2-25\}=192$

${(5+2x)}^2=49$

$5+2x=7$

$x=1$

Its thickness is 1 cm.