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Aim: How do we find the area of a sector and length of an arc in a circle?

Aim: How do we find the area of a sector and length of an arc in a circle?. Do Now: Find the area of a sector with a central angle of 60 degrees and a radius of 10.  Express answer to the nearest tenth.

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Aim: How do we find the area of a sector and length of an arc in a circle?

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  1. Aim: How do we find the area of a sector and length of an arc in a circle? Do Now: • Find the area of a sector with a central angle of 60 degrees and a radius of 10.  Express answer to the nearest tenth. • If the length of an arc is 25 cm and the circumference is 100 cm, what is the measure of the central angle? 25 n C= 100

  2. Area of a Sector When finding the area of a sector, you are actually finding a fractional part of the area of the entire circle.  The fraction is determined by the ratio of the central angle of the sector to the "entire central angle" of 360 degrees, or by the ratio of the arc length to the entire circumference. 

  3. Length of an Arc An arc is a part of a circle whose endpoints are two distinct points of the circle. A minor arc has a measure less than 180 degrees and a major arc has a measure greater than 180 degrees. To find the length of an arc, use the equation where “n” is the central angle of the arc. r n r

  4. Radians • A radian is a portion of the circle that is the length of the circle’s radius. • There are 2π radians in one circle; that means that 180 degrees = π radians • Degrees = radians x (180/π) • Radians = degrees x (π/180) • Convert 45 degrees to radians • Convert 3 radians to degrees Length of arc=r r

  5. Length of an Arc using S=Θr The formula S=Θr can also be read as arc length equals theta multiplied by r, where theta is the measure of the central angle (in radians) and r is the radius. ---------------------------------------------------------------- Use the formula S= (theta)(radius) in the following examples: 1. For a circle of radius 4 feet, find the arc length s cut off by a central angle of 12 . [A] s = 48 feet [B] s = 4 feet [C] s = 4 feet [D] s = 8 feet 2. For a circle with a radius of 5 feet, find the arc length of a central angle of 24 degrees. Leave your answer in terms of ∏.

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