Question

A solid iron rectangular block of dimension $(2.2m\times 1.2m\times 1m)$ is cast into a hollow cylindrical pipe of internal radius 35 cm and thickness 5 cm. find the length of the pipe.

• A. $20.5m$
• B. $24.5m$
• C. $22.4m$
• D. $18.4m$

Answer 1

The correct option is C $22.4m$

Volume of block $=220\times 120\times 100c.m^3$

$=2640000c{m}^3$

Let height of hollow cylinder $=h$

$\Rightarrow$ Volume $=\pi R^{2}h-\pi r^{2}h$

$r=35,R=40$

$\Rightarrow$ Volume $=\pi h[{40}^2-{35}^2]$

$\Rightarrow \pi h\times 75\times 5=2640000$

$\Rightarrow \frac{22}{7}\times h\times 375=220\times 12000$

$h=\frac{70\times 12000}{375}$

$=2240cm$

$=22.4m$.