A sphere is a 3-dimensional solid which comprises all points in space that are equi-distant from one point called the center of the sphere. The distance (sometimes the line segment itself) is called the radius of the sphere. We show sphere P below. It is named P because P is the center of the sphere. The radius r is the segment (distance) PQ.
Two important formulas help us measure the size of a sphere. volume = surface area = In the sphere shown above, suppose that r = PQ = 5 inches in length. The volume would be given by . While the surface area would be given by .
To find surface area, we use . To find the volume, we use .
We have surface area = . We solve for r by dividing both sides of this equation by . This gives us . To calculate the volume we use .