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6.8 – Areas and Sectors
Key Terms
 Area – The space taken up by a twodimensional figure or surface.
 Area is measured in square units, such as square inches, square centimeters, or square feet.
 Sector – A part of the interior of a circle bounded by an arc and the two radii that share the arc’s endpoints.
Review
Units of Area 
 Area is always listed in units “squared”
 Units may be units (units), centimeters (cm), meters (m), feet (ft), inches (in), kilometers (km), etc.
 Ex.

Arc Length and Area of a Sector Comparison 

Notes
Sectors 
 A sector of a circle is a region bounded by an arc of a circle and radii to the endpoints of the arc.
 The area of a sector is the area of the circle multiplied by the fraction of the circle covered by that sector.




Examples
Area of a Circle 
 Ex 1. If a small 12inch pizza costs $8 and a large 16inch pizza costs $12, which is the better deal?
 Steps to Find Out
 Find the area of each pizza.
 Use the area to find each pizza’s cost per square inch.
 Compare. The pizza that costs the least per square inch is the better deal.

 Large: diameter = 16 in; so, radius = 8 in
 Formula:
 Substitution:
 Simplify:
 Solve:
 Cost per Inch: ; so,

 Small: diameter = 12 in; so, 4adius = 6 in
 Formula:
 Substitution:
 Simplify:
 Solve:
 Cost per Inch: ; so,

 Result: The large pizza is about 1 cent cheaper per square inch. It doesn’t seem like much, but it will save you money in the long run if you shop “price per unit” for the lowest amount!
 For the pizza problem, you save about 88 cents per pizza if you buy the large one (201 sq in minus 113 sq in = 88 sq in).
 If each square inch is about 1 cent, multiply 1 cent by 88 sq in to get 88 cents!
 If you buy 10 pizzas, you save $8.80!

Important!
Practice (Apex Study 6.8)
 Try practice problems on Pgs 9, 27
 Mandatory: write and answer problems on Pgs 15, 28
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