Question

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

Answer 1

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

Answer 2

Answer:

(C) $6{\pi}ft$.

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 $\frac{3\pi}{4}$ radians. Then the length of the arc  is given by:

Length of the arc=radius×angle in radians

⇒Length of the arc=$8{\times}\frac{3\pi}{4}$

⇒Length of the arc=$6{\pi}ft$

Therefore, the length of the arc is $6{\pi}ft$.