Question Number 147146 by mathdanisur last updated on 18/Jul/21
Answered by mr W last updated on 18/Jul/21
$${h}=\frac{\mathrm{2}{S}}{{a}}=\frac{\mathrm{2}×\mathrm{12}}{\mathrm{4}}=\mathrm{6}\:{sm} \\ $$$${V}=\mathrm{2}\pi×\mathrm{12}×\frac{\mathrm{6}}{\mathrm{3}}=\mathrm{48}\pi\:{sm}^{\mathrm{3}} \\ $$
Commented by mathdanisur last updated on 18/Jul/21
$${thankyou}\:{Sir} \\ $$
Answered by Olaf_Thorendsen last updated on 18/Jul/21
$${a}\:=\:\mathrm{BC},\:{h}\:=\:\mathrm{AH}\:\left(\mathrm{the}\:\mathrm{height}\right),\:\mathrm{BH}\:=\:{x} \\ $$$$ \\ $$$$\mathrm{V}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi{h}^{\mathrm{2}} {x}+\frac{\mathrm{1}}{\mathrm{3}}\pi{h}^{\mathrm{2}} \left({a}−{x}\right) \\ $$$$\mathrm{V}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi{h}^{\mathrm{2}} {a} \\ $$$$\mathrm{S}\:=\:\frac{\mathrm{1}}{\mathrm{2}}{ah}\:\Rightarrow\:{h}\:=\:\frac{\mathrm{2S}}{{a}} \\ $$$$\mathrm{V}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi\frac{\mathrm{4S}^{\mathrm{2}} }{{a}^{\mathrm{2}} }{a}\:=\:\frac{\mathrm{4}\pi\mathrm{S}^{\mathrm{2}} }{\mathrm{3}{a}} \\ $$$$\mathrm{V}\:=\:\frac{\mathrm{4}\pi×\mathrm{12}^{\mathrm{2}} }{\mathrm{3}×\mathrm{4}}\:=\:\mathrm{48}\pi\:\approx\:\mathrm{150},\mathrm{80}\:{cm}^{\mathrm{3}} \\ $$
Commented by mathdanisur last updated on 18/Jul/21
$${Thankyou}\:{Sir} \\ $$