Given:
volume = 1928π m^3
And the formula of the volume for the sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Substitute the value of the volume:
[tex]1928\pi=\frac{4}{3}\pi r^3[/tex]
Simplify:
[tex]\begin{gathered} 1928\pi\cdot\frac{3}{4\pi}=\frac{4}{3}\pi r^3\cdot\frac{3}{4\pi} \\ \frac{5784}{4}=r^3 \\ r^3=1446 \end{gathered}[/tex]
And solve for r:
[tex]r=\sqrt[3]{1446}=11.31[/tex]
Next, the surface area is given by:
[tex]SA=4\pi r^2[/tex]
Substitute the values:
[tex]SA=4(3.14)(11.31)^2=1606.9[/tex]
Answer: 1606.9 m^2
