Question

What length of a solid cylinder 2cm in diameter must be taken to recast into a hollow cylinder of length 16cm, external diameter 20cm and thickness 2.5mm?

Answer 1

Length of hollow cylinder (h) = 16 cm
External diameter = 20 cm
$\therefore$ External radius (R) = $\frac{20}{2}$= 10 cm
Thickness of iron = 2.5 mm
$\therefore$ Internal radius (r) = 10 - 0.25 = 9.75 cm
$\therefore$ Volume of iron = $\pi h(R^2-r^2)$
=$\frac{22}{7}\times 16\times \left(19.75\right)\left(0.25\right)c{m}^3$
=$\frac{352}{7}\times 4.9375c{m}^3$
Now volume of iron = $\frac{352}{7}\times 49375c{m}^3$
Diameter of solid cylinder = 2 cm
$\therefore Radius\left(r\right)=\frac{2}{2}=1cm$
Let h be the length, then
Volume = $\pi r^{2}h$
$\therefore \pi r^{2}h=\frac{352}{7}\times 4.9375$
$\Rightarrow h=\frac{22}{7}\times 1\times 1\times h=\frac{352}{7}\times 4.9375$
$\Rightarrow h=\frac{352}{7}\times 4.9375\times \frac{7}{22}$
= 16 $\times$4.9375 = 79 cm