Question

In a circle with a radius of 7 feet, the radian measure of the central angle subtended by an arc with a length of 4 feet is ? The area of the sector formed by the arc is ? square feet.

Assume π = 3.14, and round your answers to the nearest hundredth.

Answer 1

s=rtheta==>theta=s/r
4/7=theta
a=1/2*r^2*theta
a=(1/2)(49)(4/7)
a=14 feet

Answer 2

4/7 or .51 radians b) 14 square feet

Explanation:

Radius: 7 feet

Arc length: 4 feet

Sector Area: ?

1) Since the central angle is proportional to the radius, there can be derived a formula to find it out.

L = r*α

4=7.α

4/7=7/7.α

4/7=α

2) To find the Circular Sector we need a relation between the angle, the Circle Area.

`(2\pi)/(\alpha )=(\pi r^(2))/(l) \\  (2\pi)/(4/7)=(\pi r^(2))/(l) \\ \\2\pi l=4/7\pi r^(2) :\pi \\ 2l=4/7r^(2) \\ 2l=4/7*49\\  2l=28\\ 2l/2=28/2\\ l=14 feet`