arcs & sectors basic definitions calculating arc length unit assessment level questions...
TRANSCRIPT
Arcs & Sectors
Basic Definitions
Calculating Arc Length
Unit Assessment
Level Questions
Calculating Sector Area
Course level
questions
Definitions – Make sure you know these
Angle Fraction
Major and Minor Arcs& Arc Length
The angle between two radii is critical in these calculations because the size of the angle is directly proportional to the arc length and the sector area. The angle is usually called and the fraction of the circle formed by this angle is called the angle fraction it is
Sectors & Sector Areas
360
Angle Fraction
Major and Minor Arcs& Arc Length
An arc is a part of the circumference of a circle joining two points. Here the shorter arc joining A to B is the minor arc. The longer arc is the major arc. You will be expected to calculate the lengths of these arcs
Sectors & Sector Areas
The region enclosed by an arc and its two radii is called a sector. You need to be able to calculate such areas.
Calculating Arc Length
These are very routine questions which you need to be able to work through quickly and accurately.
rArcAB 2
360
The arc length formula lets you calculate the length IFyou know the radius and the angle between the radii.The formula is:
The arc length is this fraction
Of the circumference
=80°
Example: calculate the minor arc length AB7cm
714.32
236036080
rArcAB
)3(77.9 sfcm
You will often find
slight differences
in rounding if you
use the built in
calculator value of .
Calculating Sector AreaThese are very routine questions which you need to be able to work through quickly and accurately.
2
360rSectorAB
The sector area formula lets you calculate the area IFyou know the radius and the angle between the radii.The formula is:
The sector area is this fraction
Of the circle area
=80°
Example: calculate the sector area shown7cm
4914.336036080
2
rSectorAB
)3(2.34 2 sfcm
Unit Assessment Arcs/Sectors questions
=65°
Example: calculate the minor arc length AB5.3m
=65°
Example: calculate the sector area shown5.3m
3.514.32
236036065
rArcAB
)3(01.6 sfcm
236065
2
3.514.3360
rSectorAB
)3(9.15 2 sfcm
Course Level Arcs/Sectors questionsA circle has a segment removed as shown.
The radius of the circle is 10 cm and the angle AOB = 60°. Calculate the area of the segment
When solving these questions make sure you have a strategy and get used to the fact that you will have to make use of skills covered in other parts of the courseStrategy,
Notice that the triangle is equilateral and calculate its area.Calculate the area of the complete sectorSubtract the triangle area to leave the segment area.
Area of Equilateral Triangle is ½ bh = ½ 5 53 = 2532 (can you show why?)Area of SectorAB = 60360100 = 1006 and collecting these together:
2325
6100_ AreaSegment
)3(7.30 2 sfcm