Why is the area of a circle A=π*r^2?

Question

If we get it by using integral, then why π is defined as 180°?

How do you get c=2*π*r ?

Answer 1

Using integration:-
Consider circle centre (0,0) and radius r.
Concentric strip at radius x and width ∂x
Area of strip = 2.π.x.∂x
Area of circle = ∫ 2.π.x.dx from 0 to r
Area of circle = [ 2.π.x² / 2 ] from 0 to r
Area = π.r²

Answer 2

π is NOT defined as 180 degrees
π is defined as the ratio between the circumference of a circle and its diameter. it is a curious mathematically provable fact that this number is constant for any circle you take.

what you are talking about is the radian system of angle measurement. in this system, a full circle is 2π radians
so "π radians" are equal to 180 degrees

Answer 3

?r^2 = A if r = 3.0 cm A = ?*3^2 A = 9? if r = 2.8 A = ?*2.8^2 A = 7.84? multiplying out via 3.14 A = 28.26 cm^2 for the 1st 3 cm radius circle A = 24.6176 cm^2 the version in reported quantities is 3.6424 cm^2, so because it somewhat is the section decrease.

Answer 4

the equation for a circle centered at the origin with radius r is

y^2+x^2=r^2

solving for the positive y yeilds a semicircle

y=sqrt(r^2-x^2)

taking the integral from -r to r under this curve yields (pi*r^2)/2

multipling by 2 to get the area of a full circle gives
A=pi*r^2

Answer 5

c = 2πr
c = 2π(1)
2π = circumference of unit circle.

Now relate the angle to the circumference:
2π = 360 degrees since an enter circle is 360 deg

therefore π = 180 deg

Answer 6

How do you get c=2*π*r ?
again, by using integrals

Answer 7

Como is right. using integration to solve for the area of a circle by basicall adding all the areas in the circle is the very answer to your question.

Answer 8

pi is not defined as 180 degrees...