Arc Length & Area of a Sector

7.4: 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 Blank

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?

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Area of a Sector

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 Blank

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 Blank

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