Mingshern’s Blog

    We all learn that area of a circle is given by the formula π r², but, have you ever wonder how did that formula derived from? Today, afternoon just now, Farhan messaged me and gave me a question… Why is the area of a circle π r² and why is the volume of a sphere (4/3)π r³? I think its an interesting question and below is my attempt to explain why the formulas are so… I hope its the correct logic, concept and method… =)

Why is the area of a circle π r² ?

Why is the volume of a sphere
(4/3)π r³?

    There… those are the two proofs for the formulas… I used integration to prove it… There might be other ways… In fact, i tried to prove it through a few other ways and i can still get the formulas, but they basically involve integration… For example, in calculating the area under graph for the area of circle, since its a triangle, you can just find the area which is half times base times height, which is (1/2)(r)(2π r)=π r². And for the volume of sphere, i tried a different way by defining the x as distance from the end of the sphere into the center and to the other end… And i still get the same formula… So i guess the prove is valid… Hope that its not just coincidental… =)

    Well, I hope that this post will be beneficial to those reading it… At least, it probably satisfy your curiosity… I got into a lot of hassle trying to making it look nice… (I typed the equations using a built-in equation editor in MSWords… I didn’t know MSWords have it until today… Took some time to get it done…) Friendster blog have some problem with picture arrangements… Therefore I decided to type it all out in MSWords and taking a screenshot of it… I hope you all wont mind the green wavy underline, present in the volume of sphere proof… And, for those who wonder, yeah… i did it myself… I did not copy it from any webpage or whatever… Any similarity is purely coincidence… =P 

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