Given:
The volume of the sphere is
[tex]V=1928\pi m^3[/tex]Required:
We need to find the surface area of the sphere.
Explanation:
Consider the volume of the sphere formula.
[tex]V=\frac{4}{3}\pi r^3[/tex][tex]Substitute\text{ }V=1928\pi\text{ in the formula.}[/tex][tex]1928\pi=\frac{4}{3}\pi r^3[/tex][tex]Multiply\text{ both sides by }\frac{3}{4\pi}\text{ of the equation.}[/tex][tex]1928\pi\times\frac{3}{4\pi}=\frac{4}{3}\pi r^3\times\frac{3}{4\pi}[/tex][tex]1446=r^3[/tex]Take cube root on both sides of the equation.
[tex]r=11.31[/tex]Consider the surface area formula.
[tex]S=4\pi r^2[/tex]Substitute r =11.31 in the formula.
[tex]S=4\times3.14\times(11.31)^2[/tex][tex]S=142.05[/tex][tex]S=142.1m^2[/tex]Final answer:
The surface area of the sphere is
[tex]142.1m^2[/tex]