What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?
What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?

External diameter of hollow cylinder = 20 cm

So, it’s radius = 10 cm = R

Thickness = 0.25 cm

the internal radius

    \[=\text{ }\left( 10\text{ }-\text{ }0.25 \right)\text{ }=\text{ }9.75\text{ }cm\text{ }=\text{ }r\]

Length of cylinder (h) = 15 cm

Now,

Volume

    \[\begin{array}{*{35}{l}} =\text{ }\pi h\text{ }\left( {{R}^{2~}}\text{ }{{r}^{2}} \right)\text{ }=\text{ }\pi \text{ x }15\left( {{10}^{2}}~\text{ }{{9.75}^{2}} \right)\text{ }=\text{ }15\text{ }\pi \text{ }\left( 100\text{ }\text{ }95.0625 \right)  \\ =\text{ }15\text{ }\pi \text{ x }4.9375\text{ }c{{m}^{3}}  \\ \end{array}\]

Diameter of the solid cylinder = 2 cm

so, radius (r) = 1 cm

Let h be the length of the solid cylinder,

Volume

    \[\begin{array}{*{35}{l}} =\text{ }\pi {{r}^{2}}h\text{ }=\text{ }\pi {{1}^{2}}h\text{ }=\text{ }\pi h\text{ }c{{m}^{3}}  \\ \pi h\text{ }=\text{ }15\text{ }\pi \text{ x }4.9375  \\ h\text{ }=\text{ }15\text{ x }4.9375  \\ h\text{ }=\text{ }74.0625  \\ \end{array}\]

Thus, the length of solid cylinder = 74.0625 cm