"Calculation of arc length and sector area" PPT courseware

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"Calculation of arc length and sector area" PPT courseware

1. The figure formed by an arc and two radii passing through the endpoints of the arc is called ________.

2. In a circle with radius r, assuming that the length of the arc subtended by the central angle of n° is l, and the area of ​​the sector with central angle of n° is S, then:

(1) Arc length formula l = ________;

(2) The formula for sector area is S=________ or S=________.

3. The line connecting the vertex of a cone to any point on the circumference of the base is called the _________ of the cone. The line segment between the vertex of a cone and the center of the base is called the _________ of the cone.

1. (3 points) If the radius of a sector is 1 and the arc length is π3, then the size of the central angle of the sector is ()

A. 30°B． 45°

C． 60° D． 90°

2. (3 points) The central angle of a sector is 60°, and the arc length it corresponds to is 2π cm. Then the radius of this sector is ()

A. 6 cm b． 12cm

C． 23cm D.6cm

3. (8 points) As shown in the figure, the radius O1A of the large circle O1 is the diameter of the small circle O2, and the other radius O1C of ⊙O1 intersects ⊙O2 at point B. Prove: The lengths of AB� and AC� are equal.

4. (3 points) The central angle of a sector is 120° and the radius is 3, then the area of ​​this sector is ________ (the result retains π).

5. (3 points) It is known that the area of ​​the sector is 12π and the radius is 6, then its central angle is equal to ________ degrees.

6. (3 points) It is known that the arc length of a sector is 4π and the radius is 3, then the area of ​​this sector is ________.

7. (3 points) The central angle of the sector is 120° and the arc length is 6π cm. Then the area of ​​this sector is __________.

11. (2013·Liaocheng) Consider the earth as a sphere with a smooth surface. Suppose that a circle of steel wire is wound tightly along the equator of the earth, and then the steel wire is lengthened so that the steel wire circle is 16 cm higher than the sphere along the equator. Then the steel wire needs to be lengthened approximately ()

A. 102 cm B． 104cm

C． 106 cm D. 108cm

12． As shown in the figure, the diameter of the semicircle AB = 10, P is a point on AB, points C and D are the three equal points on the semicircle, then the area of ​​the shaded part in the figure is equal to ________.

13. As shown in the figure, the length of the cone's busbar is OA=8, and the radius of the base is r=2. If a bug starts from point A, crawls around the side of the cone for a week and then returns to point A, then the length of the shortest route that the bug crawls is yes________.

14． (10 points) As shown in the figure, it is known that the side length of each small square is 1 cm, O, A, and B are all at the vertices of the small square. The sector OAB is the side expansion of a certain cone.

(1) Calculate the area of ​​the expanded side view of the cone;

(2) Find the base radius of this cone.

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Update Time: 2024-10-03

This template belongs to Mathematics courseware Hebei Education Edition Ninth Grade Mathematics Volume 1 industry PPT template

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