### Video Transcript

What is the diameter of a sphere whose
surface area is 36π square centimeters?

In this question, weβve been given the
surface area of a sphere and asked to use this to determine its diameter. We recall that the general formula for
finding the surface area of a sphere is four ππ squared. So by equating these two pieces of
information, we can form an equation that will enable us to determine firstly the radius of
the sphere. We have the equation four ππ squared
equals 36π. And we can now solve this equation. Firstly, we can cancel a factor of π on
each side. We can then divide each side of the
equation by four to leave π squared on the left-hand side and nine on the right-hand
side. So we now have the equation π squared is
equal to nine.

We solve this equation by square
rooting. And weβre only going to take the positive
value here because π has a physical meaning as the radius of the sphere. Nine is a square number, and its square
root is three. So we found that the radius of the sphere
is three centimeters. We must be careful, though, because it
wasnβt the radius of the sphere that we were originally asked to find. It was the diameter. But thatβs no problem because we know
that the diameter of a sphere is twice its radius. So if the radius is three, the diameter
will be six. Weβve solved the problem, and the
diameter of the sphere whose surface area is 36π square centimeters is six centimeters.