Question

The dimensions of a solid iron cuboid are 4.4 m $\times 2.6m\times$ 1.0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe.

Answer 1

Given,

dimension of cuboid = 4.4 m $\times 2.6m\times$ 1.0 m

Inner radius of pipe 'r' = 30 cm

Thickness of pipe = 5 cm
$\therefore$ Outer radius = 30 + 5
$\Rightarrow$ R = 35 cm

Now, Vol. of hollow pipe = Vol. of cuboid

$\pi h(R^2-r^2)=l\times b\times h$ $[\because \pi =\frac{22}{7}]$

$\frac{22}{7}\times h[{35}^2-{30}^2]=4.4\times 2.6\times 1\times 100\times 100\times 100$

$\frac{22}{7}\times h\times 65\times 5=44\times 26\times 1\times 100\times 100$

h = $\frac{44\times 26\times 100\times 100\times 7}{22\times 65\times 5}$

h= 11200 cm

h=112 m $[\because 1m=100cm]$

Hence, length of pipe =112m.