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?

Explanation

Volume of a cylinder `= pi r^2h`
Radius of the solid cylinder `= 1 cm`
So
Volume of the solid cylinder `= pi 12h = pi h cm^3`
Let’s assume the length of the solid cylinder as `h`
And,
Volume of the hollow cylinder `= pi h(R^2– r^2)`
Thickness of the cylinder `= (R – r)`
`0.25 = 10 – r`
So, the internal radius of the cylinder is `9.75 cm`
Volume of the hollow cylinder `= pi xx 16 (100 – 95.0625)`
Volume of the solid cylinder = volume of the hollow cylinder
`pi h = pi xx 16(100 – 95.06)`
`h = 79.04 cm`
Therefore, the length of the solid cylinder is `79.04 cm`.