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.

Accepted Solution

To solve this, we are going to use the surface are of a sphere formula: [tex]A=4 \pi r^2[/tex]
[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]
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=+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.