Question

A solid iron cuboidal block of dimensions $4.4m\times 2.6m\times 1m$ is recast into a hollow cylindrical pipe of internal radius $30cm$ and thickness $5cm$. Find the length of the pipe.

• A. $112m$
• B. $110m$
• C. $114m$
• D. $116m$

Answer 1

Answer: (A)

$112m$

Volume of rectangle $=lbh=\left(4.4\right)\left(2.6\right)\left(1\right)=11.44m^3=11440000$ cm${}^3$ ....(1)
Internal radius of cylinder $=$ $r$ cm
Outer Radius of cylinder $=$ $R$ cm
$\Rightarrow R=r+$ width
$\Rightarrow R=(30+5)$ cm $=35$ cm
Volume of hollow cylinder $=\pi (R^2-r^2)h$

$=\pi ({35}^2-{30}^2)h$

$=\pi \left(325\right)h$ cm${}^2$ ....(2)
Equating (1) and (2), we get
$\Rightarrow \pi \left(325h\right)=11440000$
$\Rightarrow h=11200cm=112$ m