The surface area of an sphere is given by the expression
[tex]A=4\pi r^2[/tex]
Since wer know the surface area, we can solve this expression for the radius, calculate it and then use it in the formula for volume given, as following:
[tex]\begin{gathered} A=4\pi r^2\rightarrow\frac{A}{4\pi}=r^2 \\ \\ \Rightarrow r=\sqrt[]{\frac{A}{4\pi}} \end{gathered}[/tex][tex]\rightarrow r=\sqrt[]{\frac{484\pi}{4\pi}}\rightarrow r=11[/tex][tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \\ \rightarrow V=\frac{4}{3}\pi(11)^3 \\ \\ \Rightarrow V=1774.7\pi\operatorname{cm} \end{gathered}[/tex]
Therefore, the correct answer is:
Option 2
