Arc Length and Area of a Sector

Arc Length & Area of a Sector

Objective: Use proportional reasoning to find arc length and area of a sector

Arc Length

Ex 1: Find the length of the minor arc

Ex 2:

Multiple Choice

A central angle measures $$230\degree$$ and its radius is 6 cm. What is the length of the arc intercepted by the angle? 

• 12.o4 cm

• 144.51 cm

• 24.08 cm

• 72.26 cm

Multiple Choice

What is the radius of a circle that has a central angle of 230 degrees and an arc length of 60 miles.

• 6.10 miles

• 74.95 miles

• 29.89 miles

• 14.95 miles

Area of a Circle & Semicircle

Area of a Quarter-Circle

If I want to find the area of an part of a circle, how would I do it?

Area of a Sector

Ex 1:

Ex. 2:

Multiple Choice

Find the area of a sector with a radius of 9ft and an angle measure of

$$132\degree$$  

• $$10.37\ ft^2$$  

• $$93.31\ ft^2$$  

• $$29.7\ ft^2$$  

• $$85\ ft^2$$  

Multiple Choice

Find the central angle of the sector of the circle with a radius of 12 ft, and a sector area of 72 square feet.

• $$12.75\degree$$  

• $$45\degree$$  

• $$57.30\degree$$  

• $$48.82\degree$$  

Fill in the Blanks

Multiple Choice

$$\pi r^2\cdot\left(\frac{d\degree}{360\degree}\right)$$ is the formula for the .................... of a circle.

• arc length

• area of a sector

• area of a segment

• circumference

Multiple Choice

The line that passes all the way across a circle thru its center is called the .................... of the circle.

• chord

• radius

• circumference

• diameter

Multiple Choice

$$r\cdot\theta\$$ is the formula for .................................... of a circle.

• the area

• the area of a segment

• the arc length

• the area of a sector

Multiple Choice

The distance around a portion of the circumference of a circle is called the .............................. of the circle..

• chord

• Arc

• Radius

• Diameter

Multiple Choice

Alison is jogging on a circular track that has a radius of 140 feet.  She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.

• 47
• 74
• 94
• 123

Multiple Choice

Find the arc length.  Leave your answer in terms of π.

• 7/4π
• 7/2π
• 1/8π
• 45π

Multiple Choice

Find the area of the dark blue sector shown at the left.  The radius of the circle is 4 units and the length of the arc (the curved edge of the sector) measures 7.85 units.  Express answer to thenearest tenth of a square unit.

• 0.3 square units
• 15.7 square units
• 19.7 square units
• 50.3 square units

Multiple Choice

Find the area of the shaded sector of circle O.  The radius is 6 inches and the central angle is 100°.  Express answer to the nearest tenth of a square inch.

• 9.2 sq. in.
• 10.5 sq. in.
• 31.4 sq. in.
• 38.2 sq. in.