Question

A cuboid shaped slab of iron whose dimensions are $55cm\times 40cm\times 15cm$ is melted and recast into a pipe. The outer radius and inner radius of the piper are $4cm$ and $1cm$ respectively. Find the length of the pipe.

Answer 1

Volume of material of cuboid slab $=$ volume of pipe

$r_2^2=$ outer radius

$r_1^2=$ Inner radius

$h=$ length

$\Rightarrow 55\times 40\times 15=\pi r_2^{2}h-\pi r_1^{2}h$

(Volume of cuboid $=lbh$; Cylinder $=\pi r^{2}h$)

$\Rightarrow 600\times 55=\frac{22}{7}h(16-1)$

$\Rightarrow \frac{55\times 40\times 7}{22}$

$\Rightarrow 700cm=h$

$\Rightarrow h=7m$