Which of these is the area of a sector of a circle with r = 18”, given that its arc length is 6π? A) 54.00 in2 B) 113.10 in2 C) 169.65 in2 D) 339.29 in2

Question

asked Aug 2, 2019 230k views

2 Answers

GregL · Answer 1 · 2019-08-08T18:38:43+0000

Answer:

$\text{The area of sector is }169.65 in^2$

Explanation:

Given that the radius of circle is 18 inches and length of arc is 6π

we have to find the area of sector.

The formula to find the length of arc is

$S=r\theta$

$6\pi=18* \theta$

$\theta=(6\pi)/(18)=(\pi)/(3)$

Now, to find the area of sector

$Area=(1)/(2)r^2\theta$

$A=(1)/(2)* 18^2* (\pi)/(3)=54\pi=169.646003294\sim 169.65 in^2$

$\text{Hence, the area of sector is }169.65 in^2$

Option C is correct