Question Number 94701 by i jagooll last updated on 20/May/20
$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{2} \\ $$$$ \\ $$
Commented by mr W last updated on 20/May/20
$${V}=\frac{\mathrm{4}\pi{R}^{\mathrm{3}} }{\mathrm{3}}=\frac{\mathrm{4}\pi\left(\sqrt{\mathrm{2}}\right)^{\mathrm{3}} }{\mathrm{3}}=\frac{\mathrm{8}\pi\sqrt{\mathrm{2}}}{\mathrm{3}} \\ $$
Commented by i jagooll last updated on 20/May/20
$$\mathrm{how}\:\mathrm{use}\:\mathrm{integral}\:\mathrm{sir}? \\ $$
Commented by i jagooll last updated on 20/May/20
$$\mathrm{vol}\:=\:\mathrm{8}\pi\:\underset{\mathrm{0}} {\overset{\sqrt{\mathrm{2}}} {\int}}\:\underset{−\sqrt{\mathrm{2}−\mathrm{x}^{\mathrm{2}} }} {\overset{\sqrt{\mathrm{2}−\mathrm{x}^{\mathrm{2}} }} {\int}}\:\sqrt{\mathrm{2}−\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }\:\mathrm{dy}\:\mathrm{dx}\:? \\ $$