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"Arc Length and Sector Area" Circle PPT (First Lesson)
The first part: the famous teacher’s eye-catching
Knowledge point 1 Arc length formula
The calculation formula for the arc length l subtended by the central angle of n° is l=nπR/180, where R is the radius.
Core tip: In the arc length formula, if any two quantities of l, n, and R are known, the third quantity can be found.
Knowledge point 2: Definition of sector
The figure enclosed by the two radii that form the central angle and the arc subtended by the central angle is called a sector.
Knowledge point 3: Sector area formula
(1) The formula for sector area with n° central angle: S sector = nπR2/360, where R is the radius.
(2) The formula for the area of a sector with arc length l: S sector = 1/2lR, where R is the radius.
[Typical example] As shown in the figure, in a circle with a radius of 12, the two central angles ∠AOB=60° and ∠COD=120°, connect AB and CD, and find the area of the shaded part in the figure.
Arc length and sector area PPT, Part 2 content: Basic pass
1. The central angle of a sector is 120° and the radius is 3. Then the arc length of this sector is ()
A. 4π B. 3π
C. 2π D． π
2. It is known that the length of the arc subtended by the central angle of 18° is π/5 cm, then the radius of the circle where this arc is located is ()
A. 2 cm B. 3 cm
C. 4 cm D． 5 cm
3． In a sector-shaped OAB with a central angle of 120°, the radius OA=6 cm, then the area of the sector-shaped OAB is ()
A. 6π cm2 B. 8π cm2
C. 12π cm2 D． 24πcm2
4. If the central angle of a sector is 45° and the area is 6π, then the radius of the sector is ()
A. √3 B. 2√3
C. 3√3 D. 4√3
Arc length and sector area PPT, Part 3: Capacity improvement
11. As shown in the figure, Figure 1 is part of a beautiful pattern composed of several identical figures (Figure 2). In Figure 2, the relevant data of the figure: radius OA = 2 cm, ∠AOB = 120°, then the perimeter of Figure 2 is ________cm. (The result retains π)
12. As shown in the figure, in △ABC, AC=4, rotate △ABC 30° counterclockwise around point C to get △FGC, then the area of the shaded part in the figure is ________.
13. [Core literacy question] A pulley lifting device is as shown in the figure. The radius of the pulley is 10 cm. When the radius OA of the pulley rotates counterclockwise around the axis O at an angle of 120°, the weight rises ________cm. (The result retains π)
Arc length and sector area PPT, part 4: thinking training
16. As shown in the figure, in △ABC, ∠ACB=90°, AC=BC, hypotenuse AB=2, O is the midpoint of AB, with O as the center of the circle, and the length of line segment OC as the radius, draw a sector with a central angle of 90° OEF and EF� pass through point C, and OF and OE intersect with BC and AC respectively at points G and H.
(1) Find the length of EF�;
(2) Find the area of the shaded part.
Keywords: Free download of PPT courseware for mathematics in the first volume of the ninth grade of the People's Education Press, download of arc length and sector area PPT, download of circle PPT, .PPT format;
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