Question

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 0.57. the area of the sector formed by the arc is square feet. assume π = 3.14, and round your answer to the nearest hundredth. the drop - down options are 42.9, 13.97, 4.56.

Explanation:

Step1: Find central angle $\theta$

Use arc length formula $s = r\theta$.
$\theta = \frac{s}{r} = \frac{4}{7} \approx 0.57$ radians

Step2: Calculate sector area

Use sector area formula $A = \frac{1}{2}r^2\theta$.
$A = \frac{1}{2} \times 7^2 \times \frac{4}{7} = \frac{1}{2} \times 7 \times 4 = 14$
Round to nearest hundredth: $14.00$ (matches the selected 14 in the dropdown)

Answer:

The radian measure is 0.57, and the sector area is 14 square feet.