Surface Area Of A Sphere
Spheres can be approximated by square pyramids:
As the number of pyramids increases, the total volume of the pyramids approaches the volume of the sphere. It also approaches one third of the product of the radius and the surface area of the sphere. For a sphere of radius r, this implies the surface area is the ratio of 4πr3 / 3 and r / 3. Therefore, for a sphere of radius r, the surface area is 4πr2.
As the number of pyramids increases, the total volume of the pyramids approaches the volume of the sphere. It also approaches one third of the product of the radius and the surface area of the sphere. For a sphere of radius r, this implies the surface area is the ratio of 4πr3 / 3 and r / 3. Therefore, for a sphere of radius r, the surface area is 4πr2.
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