The circumference of a sphere with radius r is given by the following formula:
[tex]C=2\pi r[/tex]Isolate r from the equation and substitute the value of C to find the raius of the sphere:
[tex]\begin{gathered} \Rightarrow r=\frac{C}{2\pi} \\ \Rightarrow r=\frac{4\pi\text{ in}}{2\pi} \\ \Rightarrow r=2\text{ in} \end{gathered}[/tex]The surface area of a sphere with radius r is given by:
[tex]S=4\pi r^2[/tex]The volume of a sphere with radius r is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]Substitute r=2 in on each formula to find the volume and surface area of the sphere:
[tex]\begin{gathered} S=4\pi(2in)^2 \\ =4\pi\cdot4in^2 \\ =16\pi in^2 \\ =50.26\ldots in^2 \\ \approx50in^2 \end{gathered}[/tex][tex]undefined[/tex]