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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 $192 {cm}^{3}$ of iron in this tube. Find its thickness.

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answer is B.

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Detailed Solution

Suppose the tube's thickness = x cm.
From the given condition, side of the square's

= (5 + 2 x) cm

Internal volume of the tube subtracted from its exterior volume equals the amount of iron it contains.

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

\Rightarrow 8 \{(5 + 2 x)^{2} - 25\} = 192

\Rightarrow (5 + 2 x)^{2} = 49

\Rightarrow 5 + 2 x = 7

\Rightarrow x = 1

So, the required thickness is 1 cm.
Thus, the correct option is 2.

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