TUC-2+Sectors+of+Circles


 * Sector of Circles **
 * (PWL 4.1 and AM 7-2) **



__**Helpful Links:**__

Information and Equations on Sectors of a Circle

Calculating Arc Length and Area

[|Practice with Sectors and Segments of a Circle]

[|Area Equations of Sectors]

[|Linear and Angular Speed]

__ **Summary:** __ This section will teach how to solve the area, radius, arc length, and central angle of a sector of a circle. Equations are usually given in the following forms:

__ **Variables:** __ s = sector, k = area, r = radius, Ɵ = central angle in radians or degrees, p = perimeter

__ **Equations:** __ s = rƟ k = 1/2r 2Ɵ k = 1/2rs p = 2r+s

This section will also teach about linear and angular speed: Ɵ must be in radians (if it's in degrees, multiple by pi/180)
 * 1 revolution = something rotates 1 time in one complete circle (ie: 300 revolutions means something rotates 300 times in one complete circle) **

__ **Variables:** __ V = linear speed, r = radius, w = angular speed, t = time, Ɵ = angle

__ **Equations for Linear Speed:** __ V = rw

__ **Equations for Angular Speed:** __ w = Ɵ /t

__ **Practice Problems:** __
 * 1) Find the included angle in radians with a radius of 15 inches and an arc length of 8 inches.
 * 2) A sector has a perimeter of 18 units and an area of 18 units^2. Determine the radius of the sector.
 * 3) A satellite in a circular orbit 1250 kilometers above Earth makes one complete revolution every 110 minutes. What is the linear speed? Assume that Earth is a sphere with a radius of 6400 kilometers.
 * 4) The circular blade on a saw has a diameter of 7.25 inches and rotates at 4800 revolutions per minute.
 * Find the angular speed of the blade in radians per second.
 * Find the linear speed of the saw teeth (in feet per second) as they contact the wood being cut.

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