Solve 0=pi(r^{2}+900/pi^{2r^4})^1/2+1/2pir(r^2+900/pi^2r4)

$$0 = \pi ( r ^ { 2 } + \frac { 900 } { \pi ^ { 2 } r ^ { 4 } } ) ^ { 1 / 2 } + \frac { 1 } { 2 } \pi r ( r ^ { 2 } + \frac { 900 } { \pi ^ { 2 } r 4 } )$$

Solve for r_4

$$r_{4}=-\frac{900r^{3}}{\pi \left(\pi r^{5}+2\sqrt{\pi ^{2}r^{6}+900}\right)}$$

$$r\neq 0\text{ and }\pi r^{5}+2\sqrt{\pi ^{2}r^{6}+900}\neq 0\text{ and }\pi \left(\pi r^{5}+2\sqrt{\pi ^{2}r^{6}+900}\right)\neq 0$$