Answer:
[tex]85.6in^2[/tex]
Step-by-step explanation:
to find the surface area we need the radius of the sphere.
We can find the radius using the formula for circumference:
[tex]C=2\pi r[/tex]
we know that the circumference is
[tex]C=16.4in[/tex]
thus
[tex]16.4in=2\pi r[/tex]
solving for r:
[tex]r=\frac{16.4in}{2\pi} \\r=2.61in[/tex]
and now that we know the radius we calculate the surface area:
[tex]SA=4\pi r^2[/tex]
substituting r:
[tex]SA=4\pi(2.61014in)^2\\SA=4\pi(6.81in^2)\\SA=85.6in^2[/tex]
the surface area is equal to [tex]85.6in^2[/tex]
