Question

What length of solid cylinder 2 cm in diameter must be taken to be cast into a hallow cylinder of exterior diameter 12cm,0.25cm thick,15cm long.

Answer 1

$\bold{FOR \: SOLID \: CYLINDER}$

$\mathsf{Diameter \: d = 2cm}$

$\mathsf{Radiud \: r = \dfrac{2}{2}}= 1 cm$

$\huge \boxed{\mathsf{VOLUME = \pi r^{2} h}}$

$\mathsf{VOLUME = \dfrac{22}{7} \times 1^{2} \times h}$

$\huge \boxed{\mathsf{VOLUME = \dfrac{22}{7} h}}$

$\bold{FOR \: HOLLOW \: CYLINDER}$

$\mathsf{External \: Diameter \: d = 12cm}$

$\mathsf{Radius \: R = \dfrac{12}{2}= 6 cm}$

$\mathsf{Thickness = 0.25cm}$

So,

$\mathsf{Internal \: Radius \: r =6 - 0.25 = 5 .75cm}$

$\huge \boxed{\mathsf{VOLUME = \pi( R^{2} - r^{2}) h}}$

$\mathsf{VOLUME = \dfrac{22}{7} \times (6^{2} - 5.75^{2} )\times 15}$

$\mathsf{VOLUME = \dfrac{22}{7} \times (36 - 33.06) \times 15}$

$\mathsf{VOLUME = \dfrac{22}{7} \times 2.94 \times 15}$

$\huge \boxed{\mathsf{VOLUME = 138.6 cm^{2}}}$

$\large \bold{ACCORDING \: TO \: QUESTION }$

The solid cylinder is melted and recasted into a hollow cylinder therefore, there volumes will be same so,

$\large \boxed{Volume \: of \: solid \: cylinder = Volume \: of \: hollow \: cylinder }$

So,

$\mathsf{\dfrac{22}{7} \times h= 138.6 }$

$\mathsf{\dfrac{138.6 \times 7}{22} = h }$

$\huge \boxed{\mathsf{HEIGHT = 44.1cm}}$