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Question Number 147146 by mathdanisur last updated on 18/Jul/21

Answered by mr W last updated on 18/Jul/21

h=((2S)/a)=((2×12)/4)=6 sm  V=2π×12×(6/3)=48π sm^3

$${h}=\frac{\mathrm{2}{S}}{{a}}=\frac{\mathrm{2}×\mathrm{12}}{\mathrm{4}}=\mathrm{6}\:{sm} \\ $$$${V}=\mathrm{2}\pi×\mathrm{12}×\frac{\mathrm{6}}{\mathrm{3}}=\mathrm{48}\pi\:{sm}^{\mathrm{3}} \\ $$

Commented by mathdanisur last updated on 18/Jul/21

thankyou Sir

$${thankyou}\:{Sir} \\ $$

Answered by Olaf_Thorendsen last updated on 18/Jul/21

a = BC, h = AH (the height), BH = x    V = (1/3)πh^2 x+(1/3)πh^2 (a−x)  V = (1/3)πh^2 a  S = (1/2)ah ⇒ h = ((2S)/a)  V = (1/3)π((4S^2 )/a^2 )a = ((4πS^2 )/(3a))  V = ((4π×12^2 )/(3×4)) = 48π ≈ 150,80 cm^3

$${a}\:=\:\mathrm{BC},\:{h}\:=\:\mathrm{AH}\:\left(\mathrm{the}\:\mathrm{height}\right),\:\mathrm{BH}\:=\:{x} \\ $$$$ \\ $$$$\mathrm{V}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi{h}^{\mathrm{2}} {x}+\frac{\mathrm{1}}{\mathrm{3}}\pi{h}^{\mathrm{2}} \left({a}−{x}\right) \\ $$$$\mathrm{V}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi{h}^{\mathrm{2}} {a} \\ $$$$\mathrm{S}\:=\:\frac{\mathrm{1}}{\mathrm{2}}{ah}\:\Rightarrow\:{h}\:=\:\frac{\mathrm{2S}}{{a}} \\ $$$$\mathrm{V}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi\frac{\mathrm{4S}^{\mathrm{2}} }{{a}^{\mathrm{2}} }{a}\:=\:\frac{\mathrm{4}\pi\mathrm{S}^{\mathrm{2}} }{\mathrm{3}{a}} \\ $$$$\mathrm{V}\:=\:\frac{\mathrm{4}\pi×\mathrm{12}^{\mathrm{2}} }{\mathrm{3}×\mathrm{4}}\:=\:\mathrm{48}\pi\:\approx\:\mathrm{150},\mathrm{80}\:{cm}^{\mathrm{3}} \\ $$

Commented by mathdanisur last updated on 18/Jul/21

Thankyou Sir

$${Thankyou}\:{Sir} \\ $$

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