Select the correct answer from each drop-down menu. 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 Ο€ = 3.14, and round your answers to the nearest hundredth.

Accepted Solution

In a circle, the number of radians is proportional to the relative length of the arc, in comparison to the radius. We have that if we denote by x the radians, the following proportionality holds, relating angles and lengths:
[tex] \frac{x}{2\pi} = \frac{4}{2 \pi 7} [/tex]
because the total of angles in radians is 2pi and the total circumference is 2pi times the radius. Hence, by solving for x we get: x=4/7=0.57 rad

We also have that the area is proportional to the angles. The total are is [tex]\pi r^2[/tex]. Hence, A=[tex] \frac{4}{2 \pi 7 } *\pi* 7^2= 14 square feet.[/tex]