Question Number 216478 by Tawa11 last updated on 08/Feb/25
Commented by mr W last updated on 09/Feb/25
$${the}\:{vertex}\:{of}\:{the}\:{cone}\:{may}\:{touch}\: \\ $$$${any}\:{point}\:{of}\:{one}\:{end}\:{of}\:{the}\:{cylinder}, \\ $$$${we}\:{always}\:{have} \\ $$$${V}_{{S}} =\mathrm{2}{V} \\ $$
Answered by A5T last updated on 09/Feb/25
$$\mathrm{Volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone},\mathrm{V}=\frac{\pi\mathrm{R}^{\mathrm{2}} \mathrm{h}}{\mathrm{3}} \\ $$$$\mathrm{Volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cylinder}=\pi\mathrm{R}^{\mathrm{2}} \mathrm{h} \\ $$$$\Rightarrow\mathrm{Volume}\:\mathrm{of}\:\mathrm{shaded}\:\mathrm{space}=\pi\mathrm{R}^{\mathrm{2}} \mathrm{h}−\frac{\pi\mathrm{R}^{\mathrm{2}} \mathrm{h}}{\mathrm{3}}=\frac{\mathrm{2}\pi\mathrm{R}^{\mathrm{2}} \mathrm{h}}{\mathrm{3}} \\ $$$$=\mathrm{2V} \\ $$
Commented by Tawa11 last updated on 08/Feb/25
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{got}\:\:\mathrm{2V}\:\:\mathrm{sir}. \\ $$$$\mathrm{You}\:\mathrm{made}\:\mathrm{a}\:\mathrm{mistake}\:\mathrm{sir}.\:\:\:\mathrm{2}\:\:×\:\frac{\pi\mathrm{R}^{\mathrm{2}} \mathrm{h}}{\mathrm{3}}\:\:\:=\:\:\:\mathrm{2V}. \\ $$$$\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{sir}. \\ $$
Commented by A5T last updated on 09/Feb/25
$$\mathrm{It}\:\mathrm{was}\:\mathrm{a}\:\mathrm{mistake},\:\mathrm{thanks}. \\ $$