why do we use the symbol pi when finding out the area of a circle?

Question

i am just wondering

Answer 1

We use a symbol rather than a number because we cannot write the number exactly using our normal methods. Neither as a fraction (though 22/7 is a useful appoximation) nor as a decimal (3.142 is a common approximation). Such numbers are called 'irrational' in mathematics. Using aa marker lets the reader substitute a value of sufficient accuracy for whatever purpose they have.

The constant is named "π" because it is the first letter of the Greek words περιφέρεια 'periphery' and περίμετρος 'perimeter', i.e. 'circumference'.

Answer 2

pi is the ratio of the circumference to the diameter (like was written in another answer), but to answer the question we need to say why this is used in the area calculation.

A visual way to see this is to cut a circle into 20 or 30 small pie-shaped slices (called a sector of a circle). Arrange them so that the long parts (radii) are touching, but the rounded parts alternate being up and down. When you are done you will see a shape that is something like a rectangle with curvy top and bottom sides. The short sides of the rectangle are the length of the radius. The long sides are the length of half the circumference. c=(pi)d or since d=2r, c=2(pi)r Half of 2(pi)r is (pi)r, so (pi)r is the length of the long sides. The short side r times the long side (pi)r is (pi) r^2. So the area of a circle is (pi)r^2.

The fact that the shape you made isn't exactly a rectangle might bother you, but think of cutting the circle into 10,000 pie shapes which would make the shape look much less curvy and more like a rectangle.

Answer 3

Ok, the lame answer- because it works. But think of this: If we had 6 fingers on each hand we would probably have a base 12 number system. This would be really great for weights and measures, and I am sure we would add two more numbers to make twelve written as 10 (as the school house rock song "twelvetoes" suggests). This means that all of our mathmatics would be different, so pi would be another number that worked in this equation. Subjective math? You bet your sweet five fingered bippy...

Answer 4

Because the true value of pi is an irrational number, or one that cannot be completely and accurately described using our limited number system, pi can never be accurately described as a fraction (22/7 for example) or as a decimal without going on forever with the digits after the decimal point.

Answer 5

The first person is on the right track, but technically, pi is the ratio of the circumference of a circle to its diameter.

Answer 6

The formula for the area of a circle is A = π r² The formula for the circumference of a circle is C = 2 π r The thing you need to know to get from A to C is r. Solving A = π r² for r, r = √(A/π) Um… that means divide the value you have for the area by π, and whatever you get, take the square root. That’s r. Now, to get C, multiply the value you get for r by 2 and multiply that by π. Nothing complex... just a little bit of algebra.... you can do it. Or you can wait for somebody to do it for you.

Answer 7

Take anything circular in your house.. measure the circumference and the diameter.. and then divide the circumference by the diameter.. If you don't get anything close to 3.14, then either the thing isn't circular enough or you don't know how to measure the circumference/diameter of an object!

Answer 8

pi is a natural ratio in nature of the diameter of a circle to it's circumference.

Answer 9

It's easier than writing out 2 x 3.5 x 3.14 = 1/2 of 3.14x. (this isn't a real problem, by the way.)
At least, that's why I use the symbol.

Answer 10

it was just what was discovered that worked. plus the formula is radius times radius times pi = area