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{\displaystyle V(Q)=\int _{0}^{R}\int _{0}^{2\pi }\int _{0}^{\pi }r^{2}\,\mathrm {sen} \varphi \,d\varphi d\theta dr=\int _{0}^{R}r^{2}\int _{0}^{2\pi }\int _{0}^{\pi }\mathrm {sen} \varphi \,d\varphi d\theta dr=}{\displaystyle =\int _{0}^{R}r^{2}\int _{0}^{2\pi }(-cos(\pi )+cos(0))\,d\theta dr=2\int _{0}^{R}r^{2}\int _{0}^{2\pi }1\,d\theta dr=} {\displaystyle =2\int _{0}^{R}r^{2}(2\pi -0)\,dr=4\pi \int _{0}^{R}r^{2}\,dr=4\pi \left[{\frac {r^{3}}{3}}\right]_{0}^{R}={\frac {4}{3}}\pi R^{3}}
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