A-region-is-enclosed-by-curves-x-2-4y-x-2-4y-x-4-amp-x-4-V-1-is-the-volume-of-the-solid-obtained-by-rotating-the-above-region-round-the-y-axis-Another-regions-consists-of-points-x-y-satisf

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Question Number 144771 by imjagoll last updated on 29/Jun/21

$$\mathrm{A}\mathrm{region}\mathrm{is}\mathrm{enclosed}\mathrm{by}\mathrm{curves}$$$${\mathrm{x}}^2=4\mathrm{y},{\mathrm{x}}^2=-4\mathrm{y},\mathrm{x}=4\mathrm{\&}\mathrm{x}=-4$$$${\mathrm{V}}_1\mathrm{is}\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{obtained}$$$$\mathrm{by}\mathrm{rotating}\mathrm{the}\mathrm{above}\mathrm{region}\mathrm{round}$$$$\mathrm{the}\mathrm{y}-\mathrm{axis}.\mathrm{Another}\mathrm{regions}$$$$\mathrm{consists}\mathrm{of}\mathrm{points}(\mathrm{x},\mathrm{y})\mathrm{satisfying}$$$${\mathrm{x}}^2+{\mathrm{y}}^2⩽16,{\mathrm{x}}^2+{(\mathrm{y}-2)}^2⩾4\mathrm{and}$$$${\mathrm{x}}^2+{(\mathrm{y}+2)}^2⩾4,{\mathrm{V}}_2\mathrm{is}\mathrm{the}\mathrm{volume}$$$$\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{obtained}\mathrm{by}\mathrm{rotating}$$$$\mathrm{this}\mathrm{region}\mathrm{round}\mathrm{the}\mathrm{y}-\mathrm{axis}$$$$\mathrm{Then}{\mathrm{V}}_1=\dots$$$$$$

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