If the area of a sector is 100 ft^2 and the radius of the circle is 22 ft what is the central angle measure for that sector and what is the length of the arc

Question

asked Mar 14, 2022 142k views

1 Answer

Mrana · Answer 1 · 2022-03-20T02:45:32+0000

Answer:

$\displaystyle \theta=0.413\ rad$

L= 9.086 feet

Explanation:

Area of a Circular Sector

Given a circle of radius r, the area of a circular sector defined by a central angle θ (in radians) is given by

$\displaystyle A=(1)/(2)r^2\theta$

And the length of the arc is:

$L=\theta r$

We know the area of the sector is 100 square feet and the radius is r=33 ft, thus:

$\displaystyle 100=(1)/(2)r^2\theta$

Solving for θ:

$\displaystyle \theta=(200)/(r^2)$

$\displaystyle \theta=(200)/(22^2)$

$\displaystyle \theta=0.413\ rad$

The arc length is:

L=0.413* 22

L= 9.086 feet