Central Angles and Arcs

Question

Find the area of each sector to the nearest tenth, given its central angle, theta sign= represents the central angle in radians, and the radius of the circle.

1.) Theta=54°, r=6 in.

2.) Theta=82°, r=7.3 km

3.) Theta= 12°, r=14 yd

For the following exercises, round answers to the nearest tenth.

4.) An arc is 70.7 m long and it subtends a central angle of 2pi/7. Find the diameter of the circle.

5.) A sector has area of 15 in^2 and a central angle of 0.2 radians. Find the radius of the circle and arc length of the sector.

Mechanics- Don't round to the nearest tenth.

6.) A wheel has a radius if 3.5 feet. As it turns, a cable connected to a box winds onto the wheel. To the nearest foot, how far does the box move if the wheel turns 130°in the counterclockwise direction?

Answer 1

For 1 ,2 and 3 use the formula:  theta/360*pi*r^2