Respuesta :
Answer:
The circumference of the circle that has a diameter of 24ft is [tex] \\ C = 75.36\;ft[/tex].
Step-by-step explanation:
The circumference of a circle is given by the formula:
[tex] \\ C = 2*\pi*r[/tex] [1]
Where
[tex] \\ C[/tex] is the circle's circumference.
[tex] \\ \pi = 3.1415926535897932384626...[/tex]. It is a constant and represents the ratio between the length of the circumference to the diameter of the circle, that is, [tex] \\ \pi = \frac{C}{2*r} = \frac{C}{D}[/tex]. This number is irrational and has infinite digits.
[tex] \\ r[/tex] is the circle's radius.
The diameter of a circle is
[tex] \\ D = 2*r = 24[/tex]ft
Therefore, we can rewrite equation [1] as
[tex] \\ C = 2*r*\pi = D*\pi[/tex]
Then
[tex] \\ C = D*\pi[/tex]
[tex] \\ C = 24\;ft*\pi[/tex]
Using [tex] \\ \pi = 3.14[/tex]
[tex] \\ C = 24\;ft*3.14[/tex]
[tex] \\ C = 75.36\;ft[/tex]
Then, the circumference of the circle that has a diameter of 24ft is [tex] \\ C = 75.36\;ft[/tex].
Notice that [tex] \\ \pi[/tex] is dimensionless and, since the diameter is in ft the circumference is also represented in this unit.
