What is the diameter of a sphere whose
surface area is 36𝜋 square centimeters?
In this question, we’ve 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 𝜋𝑟 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 𝜋𝑟 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 𝑟 squared on the left-hand side and nine on the right-hand
side. So we now have the equation 𝑟 squared is
equal to nine.
We solve this equation by square
rooting. And we’re only going to take the positive
value here because 𝑟 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
wasn’t the radius of the sphere that we were originally asked to find. It was the diameter. But that’s 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. We’ve solved the problem, and the
diameter of the sphere whose surface area is 36𝜋 square centimeters is six centimeters.