contestada

In a circle with a radius of 8 ft, an arc is intercepted by a central angle of 3π4 radians.



What is the length of the arc?


2π ft

​ 3π ​ ft

​ 6π ​ ft

​ 9π ​ ft

Respuesta :

calculista
we know that

the length of a circumference=2*pi*r
for r=8 ft
the length of a circumference=2*pi*8---------> 16π ft

if 2π radians  (full circle)-------------------> has a length of 16π ft
3π/4 radians-------------------------------> X
X=3π/4*16π/2π-------------> X=6π ft

the answer is
6π ft
boffeemadrid

Answer:

(C) [tex]6{\pi}ft[/tex].

Step-by-step explanation:

It is given that In a circle with a radius of 8 ft, an arc is intercepted by a central angle of [tex]\frac{3\pi}{4}[/tex] radians. Then the length of the arc  is given by:

Length of the arc=radius×angle in radians

⇒Length of the arc=[tex]8{\times}\frac{3\pi}{4}[/tex]

⇒Length of the arc=[tex]6{\pi}ft[/tex]

Therefore, the length of the arc is [tex]6{\pi}ft[/tex].