To solve this, we are going to use the surface are of a sphere formula: [tex]A=4 \pi r^2[/tex]
where
[tex]A[/tex] is the surface area of the sphere
[tex]r[/tex] is the radius of the sphere
We know for our problem that [tex]A=2122.64[/tex] and [tex] \pi =3.14[/tex], so lets replace those vales in our formula:
[tex]A=4 \pi r^2[/tex]
[tex]2122.64=4(3.14)r^2[/tex]
[tex]2122.64=12.56r^2[/tex]
Now, we just need to solve our equation for [tex]r[/tex]:
[tex] \frac{2122.64}{12.56} =r^2[/tex]
[tex] r^2=\frac{2122.64}{12.56}[/tex]
[tex]r^2=169[/tex]
[tex]r=+or- \sqrt{169} [/tex]
[tex]r=13[/tex] or [tex]r=13[/tex]
Since the radius of a sphere cannot be a negative number, [tex]r=13[/tex].
We can conclude that the radius of a sphere with surface area 2,122.64 [tex]in^2[/tex] is 13 in.
