Respuesta :
Answer:
The circumference for circle a is [tex] \\ C = 131.9430[/tex]m.
The circumference for circle b is [tex] \\ C = 175.9240[/tex]m.
The relationship between the radius of a circle and the circumference (the distance around the circle) is constant and is the same for all circles and can be written as [tex] \\ \frac{C}{r} = 2\pi[/tex] or, in a less familiar form, [tex] \\ \frac{r}{C} = \frac{1}{2\pi}[/tex]. The number [tex] \\ \pi[/tex] is constant for all circles and has infinite digits, [tex] \\ \pi = 3.14159265358979....[/tex].
Step-by-step explanation:
The circumference of a circle is given by:
[tex] \\ C = 2*\pi*r[/tex] [1]
Where
[tex] \\ C[/tex] is the circle's circumference.
[tex] \\ r[/tex] is the radius of the circle.
And
[tex] \\ \pi = 3.141592....[/tex] is a constant value (explained below)
We can say that the distance around the circle is the circle's circumference.
The circumferences of the two circles given are:
Circle a, with radius equals to 21 meters ([tex] \\ r = 21m[/tex]).
Using [1], using four decimals for [tex] \\ \pi[/tex], we have:
[tex] \\ C = 2*\pi*r[/tex]
[tex] \\ C = 2*3.1415*21[/tex]m
[tex] \\ C = 131.9430[/tex]m
Then, the circumference for circle a is [tex] \\ C = 131.9430[/tex]m.
Circle b, with radius equals to 28 meters ([tex] \\ r = 28m[/tex]).
[tex] \\ C = 2*3.1415*28[/tex]m
[tex] \\ C = 175.9240[/tex]m
And, the circumference for circle b is [tex] \\ C = 175.9240[/tex]m.
We know that
[tex] \\ 2r = D[/tex]
That is, the diameter of the circle is twice its radius.
Then, if we take the distance around the circle and we divided it by [tex] \\ 2r[/tex]
[tex] \\ \frac{C}{2r} = \frac{C}{D} = \pi[/tex]
This ratio, that is, the relationship between the distance around the circle (circumference) and the diameter of a circle is [tex] \\ \pi[/tex] and is constant for all circles. This result is called the [tex] \\ \pi[/tex] number, which is, approximately, [tex] \\ \pi = 3.141592653589793238....[/tex] (it has infinite number of digits).
We can observe that the relationship between the radius of a circle and the circumference is also constant:
[tex] \\ \frac{C}{2r} = \frac{C}{D} = \pi[/tex]
[tex] \\ \frac{C}{2r} = \pi[/tex]
[tex] \\ \frac{C}{r} = 2\pi[/tex]
However, this relationship is [tex] \\ 2\pi[/tex].
We can rewrite it as
[tex] \\ \frac{r}{C} = \frac{1}{2\pi}[/tex]
And it is also constant.
