Question

What is the radius of a sphere if its surface area is 2,122.64 square inches? (Use 3.14 for π.) 11 in. 13 in. 121 in. 169 in.

Answer 1

To solve this, we are going to use the surface are of a sphere formula: $A=4 \pi r^2$
where
$A$ is the surface area of the sphere 
$r$ is the radius of the sphere 

We know for our problem that $A=2122.64$ and $\pi =3.14$, so lets replace those vales in our formula:
$A=4 \pi r^2$
$2122.64=4(3.14)r^2$
$2122.64=12.56r^2$
Now, we just need to solve our equation for $r$:
$\frac{2122.64}{12.56} =r^2$
$r^2=\frac{2122.64}{12.56}$
$r^2=169$
$r=+or- \sqrt{169}$
$r=13$ or $r=13$
Since the radius of a sphere cannot be a negative number, $r=13$.

We can conclude that the radius of a sphere with surface area 2,122.64 $in^2$ is 13 in.