Question

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

Answer 1

Let the length of the solid cylinder be h. Its radius $r_1$= 1 cm

Outer radius of hollow cylinder $R=\frac{20}{2}=10cm$

Thickness = 2.5 mm = 0.25 cm

So, inner radius $r=10-0.25=9.75cm$

As per the question, volume of solid cylinder = volume of the material of hollow cylinder

$\Rightarrow \pi r_1^{2}h=\pi (R^2-r^2)h$

$\Rightarrow \pi \times 1\times 1\times h=\pi \times ({10}^2-{9.75}^2)\times 16$

$\Rightarrow h=(10+9.75)\times (10-9.75)\times 16$

$=19.75\times 0.25\times 16$

$=79cm$