Question

How are the formulas for the circumference of a circle and area of a circle derived?

Answer 1

ecall that the definition of pi (π) is the circumference c of any circle divided by its diameter d. Put as an equation, pi is defined as Rearranging this to solve for c we get The diameter of a circle is twice its radius, so substituting 2r for d
If you know the area
Recall that the area a of a circle is given by Solving this for r The circumference c of a circle is Substituting r Squaring both sides to lose the radical Solving for c:

Answer 2

recall*

Answer 3

well circle is actually a sector with an angle of 2pi radians b/w it's arms
i know it sounds freaky
but it's actually that the sector tends towards the circle
and the length of the arc formula derivation can be found on sum website
the formula is
l = (angle in radians)(distance b/w the points of the locus and centre of rotation i.e. radius)
so l = (angle)r
in case of a circle angle = 2pi radians
so
l = 2*pi*r
here the arc would have tended to circumference as sector tends towards circle
so
C = 2*pi*r units

Answer 4

That is the correct answer yw

Answer 5

I know that the formula to find the circumference of a circle is C=3.14d
I know that the area of the circle formula is A=3.14r2

Answer 6

ok well then this should be a piece of cake

Answer 7

I am confused on what the answer is. How ould i answer this question simply? @ArmyBoy97

Answer 8

ummm let me see.

Answer 9

derived means to take or get (something) from something else i think

Answer 10

sin(theta) = a / c
csc(theta) = 1 / sin(theta) = c / a
cos(theta) = b / c
sec(theta) = 1 / cos(theta) = c / b
tan(theta) = sin(theta) / cos(theta) = a / b
cot(theta) = 1/ tan(theta) = b / a

Answer 11

my bad wrong question

Answer 12

that is correct @EmmaDrew94

Answer 13

lol one sec

Answer 14

i am helping two people at once

Answer 15

@ArmyBoy97 ok your just confusing me that isnt helping me at all. What is the answer thats not where the formulas derive from

Answer 16

im soryy im multitasking righht now

Answer 17

Ok wait a sec i'll try:)

Answer 18

@Here_to_Help15 he will help you im really busy

Answer 19

well im not sure if this is what your looking for.

but for circuimference, if you take the diameter and wrap it around the circle,
you would need about 3 and a little more of the diameter to completely wrap around the circle

Answer 20

@nikato deserves a medal

Answer 21

go away lol i thought you were busy @ArmyBoy97

Answer 22

ok whatever i was just trying to help not my fault your not good at math?

Answer 23

Thank you @nikato

Answer 24

you shouldnt be rude to people who try to help you

Answer 25

then no one will want to help you