Answer:
10 in
Step-by-step explanation:
So we want to consider the surface area of this sphere.
The formula for surface area of a sphere is [tex]A=4 \pi r^2[/tex].
So we have that the surface area is [tex]100 \pi[/tex].
So I'm going to replace [tex]A[/tex] in [tex]A=4 \pi r^2[/tex] with [tex]100 \pi[/tex].
[tex]100\pi=4\pi r^2[/tex]
Now our main objective here is to solve for [tex]r[/tex]:
Divide both sides by [tex]4 \pi[/tex]:
[tex]\frac{100\pi}{4 \pi}=\frac{4\pi r^2}{4 \pi}[/tex]
This gets us [tex]r^2[/tex] by itself:
[tex]25=r^2[/tex]
What number squared gives you 25? If you don't know, just take the square root of both sides giving you:
[tex]\sqrt{25}=r[/tex]
Now you can just put [tex]\sqrt{25}[/tex] in your calculator. You should get 5.
5 is the radius
The diameter is twice the radius.
So 2(5) is 10, so the diameter is 10 in.
