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Why should we use the area of circle as $\pi$ multiplied by square of radius ?

Can't we use another formula to get the specific answer? We know that $\pi$ does not equals to $\frac{22}{7}$ or $3.14$ but then why are we using it to get a approximate a wrong answer?

Why can't we deduce the accurate area or circumference of a circle? If we clear this we could get even accurate answers of the surface areas of sphere, cylinder and many other figures .

S.C.B.
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Padmanabhan M
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    What is the question? – copper.hat Feb 14 '16 at 06:24
  • check http://math.stackexchange.com/questions/187987/calculus-proof-for-the-area-of-a-circle – Win Vineeth Feb 14 '16 at 06:28
  • You might wanna go through some good geometry book. I wonder if I can recommend Elementary Geometry from an Advanced Standpoint by Edwin E. Moise, but I'm not sure. Check this book to see if it answers your question. – Saaqib Mahmood Feb 14 '16 at 06:30
  • @copper.hat -- the question seems to be ... why can't we invent some new/different formula to calculate the area of a circle. Specifically, it would be nice if we could find a formula that does not involve $\pi$, because any practical calculation using $\pi$ necessarily involves approximation and is therefore "wrong". – bubba Feb 14 '16 at 08:35
  • It seems like a perfectly reasonable question, to me, so I don't understand the downvotes (as is often the case, lately). – bubba Feb 14 '16 at 08:37
  • If we could know both the area and the radius exactly, then we would know $\pi=\sqrt{{\rm Area}/{\rm radius}^2}$ exactly. – Akiva Weinberger Feb 14 '16 at 16:37

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$\pi$, as defined in Wikipedia, is "the numerical value of the ratio of the circumference of a circle to its diameter." Thus, it's not right when you say that the value is not accurate. It is. That's how $\pi$ has been defined. To make it accurate. Other formulas that rely on the value of $\pi$ also reply on the fact that $\pi$ is nothing but the ratio of a circle's circumference to its diameter. All the algorithms and formulas that calculate the value of $\pi$ are basically created using this very fact. So, when you say we should clear this to get even accurate results, you are wrong. They did clear it, very long ago. That's how and why they created the concept of $\pi$.

MathIsNice1729
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