A solid iron rectangular block of dimensions 4.4 m, 2.6 m and 1 m is cast into

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Question

A solid iron rectangular block of dimensions 4.4 m, 2.6 m and 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe (in m).

Options:

A . 112

B . 221

C . 121

D . 211

Answer: Option A
:
A

Volume of iron
$= (440 \times 260 \times 100) c m^{3}$ .
Internal radius of the pipe
$= 30 c m$ .
External radius of the pipe
$= (30 + 5) c m = 35 c m$ .
Let the length of the pipe be $h c m$ .
Volume of iron in the pipe = (External volume) - (Internal volume)
$= [π (35)^{2} \times h - π (30)^{2} \times h] c m^{3}$

$= (π h) ((35)^{2} - (30)^{2}) c m^{3}$

$= (65 \times 5) π h c m^{3}$
Volume of iron in the pipe = Volume of iron block

$\Rightarrow (325 π h) c m^{3} = 440 \times 260 \times 100$

$h = \frac{440 \times 260 \times 100}{325} \times \frac{7}{22} c m$
$h = 11200 c m$

$h = \frac{11200}{100} = 112 m$

Hence, the length of the pipe is 112 m.

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