حل {l}{a^{2}-1=(r+b)^{2}+(frac{2sqrt{3}}{9})^{2}}{(r+b)^{2}+(frac{4sqrt{3}}{9})^{2}=a}{b^2+(frac{4sqrt{3}}{8})^2=r^2}{V=pir^3}

$$\left. \begin{array} { l } { a ^ { 2 } - 1 = ( r + b ) ^ { 2 } + ( \frac { 2 \sqrt { 3 } } { 9 } ) ^ { 2 } } \\ { ( r + b ) ^ { 2 } + ( \frac { 4 \sqrt { 3 } } { 9 } ) ^ { 2 } = a } \\ { b ^ { 2 } + ( \frac { 4 \sqrt { 3 } } { 8 } ) ^ { 2 } = r ^ { 2 } } \\ { V = \pi r ^ { 3 } } \end{array} \right.$$

حل مسائل a، r، b، V (complex solution)

$$r=\frac{i\sqrt{497497518\sqrt{29}-2577203286}}{83664}\approx 0.120657554i\text{, }a=-\frac{\sqrt{29}}{6}+\frac{1}{2}\approx -0.397527468\text{, }b=\frac{i\sqrt{497497518\sqrt{29}[phone]}}{83664}\approx 0.874390213i\text{, }V=-\frac{\pi i\sqrt{69349316890911577317\sqrt{29}-373452058399307569584}}{41997989376}\approx -0-0.005518403i$$

$$r=\frac{\sqrt{497497518\sqrt{29}[phone]}}{83664}\approx 0.866566381\text{, }a=\frac{\sqrt{29}}{6}+\frac{1}{2}\approx 1.397527468\text{, }b=\frac{\sqrt{497497518\sqrt{29}-2672545386}}{83664}\approx 0.030615248\text{, }V=\frac{\pi \sqrt{69349316890911577317\sqrt{29}+373452058399307569584}}{41997989376}\approx 2.044350619$$

$$r=-\frac{i\sqrt{497497518\sqrt{29}-2577203286}}{83664}\approx -0-0.120657554i\text{, }a=-\frac{\sqrt{29}}{6}+\frac{1}{2}\approx -0.397527468\text{, }b=-\frac{i\sqrt{497497518\sqrt{29}[phone]}}{83664}\approx -0-0.874390213i\text{, }V=\frac{\pi i\sqrt{69349316890911577317\sqrt{29}-373452058399307569584}}{41997989376}\approx 0.005518403i$$

$$r=-\frac{\sqrt{497497518\sqrt{29}[phone]}}{83664}\approx -0.866566381\text{, }a=\frac{\sqrt{29}}{6}+\frac{1}{2}\approx 1.397527468\text{, }b=-\frac{\sqrt{497497518\sqrt{29}-2672545386}}{83664}\approx -0.030615248\text{, }V=-\frac{\pi \sqrt{69349316890911577317\sqrt{29}+373452058399307569584}}{41997989376}\approx -2.044350619$$

حل مسائل a، r، b، V

$$r=\frac{\sqrt{497497518\sqrt{29}[phone]}}{83664}\approx 0.866566381\text{, }a=\frac{\sqrt{29}}{6}+\frac{1}{2}\approx 1.397527468\text{, }b=\frac{\sqrt{497497518\sqrt{29}-2672545386}}{83664}\approx 0.030615248\text{, }V=\frac{\pi \sqrt{69349316890911577317\sqrt{29}+373452058399307569584}}{41997989376}\approx 2.044350619$$

$$r=-\frac{\sqrt{497497518\sqrt{29}[phone]}}{83664}\approx -0.866566381\text{, }a=\frac{\sqrt{29}}{6}+\frac{1}{2}\approx 1.397527468\text{, }b=-\frac{\sqrt{497497518\sqrt{29}-2672545386}}{83664}\approx -0.030615248\text{, }V=-\frac{\pi \sqrt{69349316890911577317\sqrt{29}+373452058399307569584}}{41997989376}\approx -2.044350619$$