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The surface area of the sphere is given by the equation
,
where A is the surface area and r is the radius.
We want to find the volume of the sphere, which is given by the equation
,
where V is the volume and r is the radius.
Looking at these equations, we see that they both involve the sphere's radius. If we know what r is, we can calculate the volume.
We know that the sphere's surface area is . Plugging that in for A in the surface area equation, we get
, then divide by
, then divide by 4
, then take the square root of both sides
So the radius of the sphere is 3. Plugging this into the volume equation,
, simplify terms
, multiply
by 27
So the volume of the sphere is .