Question

7) A metallic sphere of radius 9cm is melted to form a cylinder of radius 6cm Find
the height of the cylinder

Answer 1

$\huge\red{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{The \ height \ of \ cylinder \ is \ 27 \ cm}$

$\huge\orange{Given:}$

$\sf{\implies{A \ metallic \ sphere \ is \ melted}}$

$\sf{to \ form \ cylinder.}$

$\sf{For, \ sphere}$

$\sf{Radius=9 \ cm}$

$\sf{For, \ cylinder}$

$\sf{Radius=6 \ cm}$

$\huge\pink{To \ find:}$

$\sf{Height(h) \ of \ the \ cylinder.}$

$\huge\green{\underline{\underline{Solution:}}}$

$\sf{For, \ sphere}$

$\sf{Radius(r)=9 \ cm}$

$\sf{For, \ cylinder}$

$\sf{Radius(R)=6 \ cm}$

____________________________________

$\sf{\implies{Formulae \ are:}}$

$\sf{Volume \ of \ Sphere=\frac{4}{3}×\pi×r^{3}}$

$\sf{Volume \ of \ Cylinder=\pi×R^{2}×h}$

$\sf{Cylinder \ is \ form \ by \ melting \ sphere.}$

$\sf{\therefore{Volume \ of \ cylinder=Volume \ of \ sphere}}$

$\sf{\therefore{\pi×R^{2}×h=\frac{4}{3}×\pi×r^{3}}}$

$\sf{\therefore{h=\frac{4×9×9×9}{3×6×6}}}$

$\sf{h=\frac{2916}{108}}$

$\sf{h=27 \ cm}$

$\sf\purple{\therefore{\tt{The \ height \ of \ cylinder \ is \ 27 \ cm}}}$