Question

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

Answer 1

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

Explanation:

It is given that In a circle with a radius of 8 ft, an arc is intercepted by a central angle of
`(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{*}(3\pi)/(4)`

⇒Length of the arc=
`6{\pi}ft`

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

Answer 2

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