Respuesta :

Answer:

The surface area of the sphere is:

[tex]Surface_{sphere}=843.6\,\, in^2[/tex]

Step-by-step explanation:

Recall the two following important formulas:

[tex]Volume_{sphere}=\frac{4}{3} \,\pi\,\,R^3\\\\Surface_{sphere}=4\,\pi\,R^2[/tex]

where R is the radius of the sphere.

Then, since we know the sphere's volume (2304 [tex]in^3[/tex]), we can calculate the sphere's radius:

[tex]Volume_{sphere}=\frac{4}{3} \,\pi\,\,R^3\\2304=\frac{4}{3} \,\pi\,\,R^3\\\frac{3\,*\,2304}{4\,\pi} =R^3\\R=\sqrt[3]{\frac{6912}{4\,\pi} } \, in\\R=8.1934\,\, in[/tex]

Now, knowing the radius, we can estimate the surface of the sphere using the other formula;

[tex]Surface_{sphere}=4\,\pi\,R^2\\Surface_{sphere}=4\,\pi\,(8.1934)^2\\Surface_{sphere}=843.6\,\, in^2[/tex]