MATH SOLVE

4 months ago

Q:
# 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

A:

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.

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.