Question

The dimension of a solid iron cuboid arw 4.4 m x 2.6 m x 1.0 m . It is melted and react into a hollow cylindrical pipe of 30cm inner radius and thickness 5 cm. Find the length of the pipe.

Answer 1

Iron : $l=44m$

$b=2.6m$

$h_1=1.0m$

Hollow cylinder : $r_1=30cm=0.3m$

$r_2=35cm=0.35m$

$h_2=?$

Volume of cuboid $=$ Volume of hollow cylinder

$l\times b\times h_1=\pi h_2(r_2^2-r_1^2)$

$4.4\times 2.6\times 1=\frac{22}{7}\times h_2\times [{\left(\frac{35}{100}\right)}^2-{\left(\frac{30}{100}\right)}^2]$

$\frac{44}{10}\times \frac{26}{10}=\frac{22}{7}\times h_2\times \frac{(35-30)(35+30)}{(100{)}^2}$

$=\frac{22}{7}\times h_2\times \frac{5\times 65}{(100{)}^2}$

$\therefore h_2=\frac{44}{10}\times \frac{26}{10}\times \frac{7}{22}\times \frac{100\times 100}{5\times 65}$

$\therefore h_2=112m$.