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

Fill in the Blanks

What is the measure of the central angle in a circle that intercepts an arc that is 18 cm in length and the radius of the circle is 7cm? Round the the nearest whole number. Numeric value only!

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

$$132\degree$$  

• $$10.37\ ft^2$$  

• $$93.31\ ft^2$$  

• $$29.7\ ft^2$$  

• $$85\ ft^2$$  

Fill in the Blanks

Find the radius of a circle that has the sector area

$68\ m^2$  and a central angle measure of  $63\degree$ . Round the the nearest hundredth.

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

Find the area of the sector shown. Round to the nearest hundredth

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.