text: is the surface area of a sphere accurate? in geometry today, we learned about the surface area of a sphere. the book said to imagine it as a baseball and take the two sections (the two stitched together parts) apart. when you look at it, it's like each part is two circles. therefore (they say), the surface area of a sphere is 4(pi)r^2. however, i closed the two circles in the book, and it seems there's extra area in there that isn't covered by the four circles.   now, for my actual question. :o is 4(pi)r^2 the formula used by actual mathematicians and scientists. can someone who has had higher level math answer this for me?  thank you. :d yes, 4πr² is the accurate, 'real' formula for the surface area of a sphere.  take a look at http://mathworld.wolfram.com/sphere.html for a pretty math-heavy explanation of spherical geometry. thumbs up to you for your curiosity and taking an interest in geometry and math!