Question

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

• A. $11.2cm$
• B. $11.2m$
• C. $112cm$
• D. $112m$

Answer 1

The correct option is D

$112m$

Since the pipe is obtained from the block, volume of both objects will be exactly equal to each other.

Volume of cuboid
$=l\times b\times h$

Volume of cylinder
$=\pi \left(\right(R_o{)}^2-\left(R_i{)}^2\right)\times h$,

where $R_o$ and $R_i$ indicate outside radius and inside radius respectively.

So,
$440\times 260\times 100=\pi \times ({35}^2-{30}^2)\times h$

[NOTE : $1m=100cm$]

$\Rightarrow 440\times 260\times 100=\pi \times (35+30)(35-30)\times h$
$\Rightarrow 440\times 260\times 100=\frac{22}{7}\times 325h$

$\Rightarrow h=\frac{440\times 260\times 100\times 7}{22\times 325}$

$\Rightarrow h=11200cm$

$\Rightarrow h=112m$

Hence, the length of the pipe is $112m$.