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

Answer:

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

Step-by-step 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.

$\frac{2\pi}{\alpha }=\frac{\pi r^{2}}{l} \\ \frac{2\pi}{4/7}=\frac{\pi r^{2}}{l} \\ \\2\pi l=4/7\pi r^{2} :\pi \\ 2l=4/7r^{2} \\ 2l=4/7*49\\ 2l=28\\ 2l/2=28/2\\ l=14 feet$