Have you wondered the same thing? I was learning about SA and Volume of 3 dimensional composite shapes at school when I thought, 'Why is the Surface Area of a Sphere 4(pi)r^2?' How did mathematicians derive this formula? Why does this formula make sense? There is actually a simple mathematic logic for the derivation of this particular formula. The formula was first found by Archimedes (my mathematician buddy). Archimedes proved that the surface area of a sphere is equal to the lateral surface area of a cylinder. The lateral surface area of a cylinder does not include the area of the two circular ends. For a sphere to nicely fit inside a cylinder, the height of the cylinder should be twice the sphere's radius, 2r. If the height of the cylinder is 2r, then its lateral surface area is: circumference x height = 2(pi)r x 2r = 4(pi)r^2 Therefore, the surface area of a sphere is equivalent to the formula above, or 4(pi)r^2. Are you mind-blowned like me? I know, mathematics has its own way of surprising us with its theories. Good luck,
0 Comments
Leave a Reply. |
Archives
May 2021
Topics
All
|