Question

A solid cuboid of iron with dimensions $53cm\times 40cm\times 15cm$ is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.

Answer 1

Given,

The outer and inner diameters of pipe are $8cm$ and $7cm$

Dimensions of a solid cuboid of iron $=53cm\times 40cm\times 15cm$

When a shape melted and recast into another shape volume will remain same.

Volume of cubical iron =volume of cylindrical pipe

$length\times breadth\times height=\pi (R^2-r^2)h$

$53\times 40\times 15=\frac{22}{7}\times (4^2-(\frac{7}{2}{)}^2)h$

$53\times 40\times 15=\frac{22}{7}\times \frac{15}{4}\times h$

$h=\frac{53\times 40\times 15\times 7\times 4}{22\times 15}$

$h=2698.18cm=27m$ [$\because 1m=100cm$]