"Arc Length and Sector Area" Circle PPT Download

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"Arc Length and Sector Area" Circle PPT Download

Part One: Thinking

We know that an arc is a part of a circle, and the arc length is a part of the circumference of the circle.

Think about it, how do you calculate the circumference of a circle with radius R?

Circumference C = 2πR

The circumference of a circle can be considered as the length of the arc subtended by the central angle of how many degrees?

What is the length of the arc subtended by a central angle of 1°?

What is the length of the arc subtended by the central angle of n°?

Arc length and sector area PPT, part 2: arc length formula

What is the length of the arc subtended by the central angle of n°?

When manufacturing a curved pipe, you must first calculate the "straightened length" according to the center line, and then cut the material. Try to calculate the straightened length L of the pipe shown in the figure (the result is an integer).

1. Are two arcs with equal arc length equal arcs?

2. As shown in the figure, there is an arc-shaped curve with a length of 12m and a central angle of 81°. What is the radius R of the circle where this arc is located (the result is rounded to the decimal point)?

In a circle with a radius of 6cm, the length of the arc subtended by the central angle of 120° is _______.

In a circle with a radius of 50cm, the length of the arc subtended by a central angle of 60° is _______.

Arc length and sector area PPT, the third part: 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.

It can be found that the area of ​​the sector is not only related to the radius of the circle, but also related to the size of the central angle of the circle that makes up the sector.

The larger the central angle, the larger the sector area.

How to calculate the area of ​​a sector with radius R and central angle n°?

Arc length and sector area PPT, part 4 content: sector area formula

The area of ​​a sector with central angle n° is

another formula

Compare the sector area formula and the arc length formula

The area of ​​a sector is equal to half the arc length times the radius.

Analogical memory: a fan can be viewed as a triangle

The arc length is considered as the base of the triangle

The radius is regarded as the height of the triangle

In this way,

The formula for the area of ​​a sector is consistent with the formula for the area of ​​a triangle.

Arc length and sector area PPT, Part 5: Related concepts of cones

We know that a cone is a geometric solid surrounded by a base and a side.

We call the line segment connecting the vertex of the cone and any point on the circumference of the base the generatrix of the cone.

What shape does the side expansion of a cone look like?

Let the length of the cone's generatrix be l and the radius of the base circle be r.

Then the radius of the side fan-shaped expansion is______.

The arc length of the fan-shaped side expansion is equal to __________, which is equal to __________.

The lateral area of ​​a cone is equal to _______________.

The total area of ​​the cone is equal to ______________.

Arc length and sector area PPT, Part 6: Calculate the length of the rotation path

An equilateral triangular wooden board with side length 1. Now roll the wooden board along the horizontal line (as shown in the figure), then the length of the path traveled by point B from the beginning to the end is __________.

The four sides of a square ABCD with a side length of 4 cm are rolled to the right along a straight line (without sliding). When the square is rolled two times, the length of the route taken by the vertex A of the square is __________cm.

Comprehensive calculation of sector area

As shown in the figure, A is a point outside the circle O with a radius of 1, and OA=2, AB is the tangent line of ⊙O, BC // OA, connecting AC, then the area of ​​the shaded part is equal to ________.

As shown in the figure, the side length of the square is a, and arcs are drawn with the two diagonal vertices as the center and a as the radius, then the area of ​​the shaded part in the figure is _______.

The sector-shaped OAB and sector-shaped OCD, whose central angles are both 90°, are stacked together as shown in the figure, connecting AC and BD. If OA=3 cm, OC =1 cm, find the area of ​​the shaded part.

Arc length and sector area PPT, Part 7: Summary

What did we learn in this lesson?

1. Arc length calculation formula:

The length of the arc subtended by the central angle of n° is

2. Sector area formula:

The area of ​​a sector with central angle n° is

3． Calculation formula in a cone:

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;

For more information about the "Arc Length and Sector Area" PPT courseware, please click on the Circle PPT Arc Length and Sector Area PPT tab.

"Arc Length and Sector Area" Circle PPT (Lesson 1):

"Arc Length and Sector Area" Circle PPT (Lesson 1) Part One Content: Learning Objectives 1. Understand the process of searching for arc length and sector area formulas. (Difficulty) 2. Be able to use the calculation formulas of arc length and sector area to perform calculations .(Key point) ... ... ... Arc length and fan...

"Arc Length and Sector Area" Circle PPT (Second Lesson):

"Arc Length and Sector Area" Circle PPT (Second Lesson) Part One Content: Famous Teacher's Key Points Knowledge Point 1 The Generatus and Height of a Cone A cone is a geometric body surrounded by a base and a side. Among them, the line connecting any point on the circumference of the cone base and the vertex of the cone is called...

"Arc Length and Sector Area" Circle PPT (First Lesson):

"Arc Length and Sector Area" Circle PPT (Lesson 1) Part One Content: Famous Teacher’s Key Knowledge Point 1 The arc length formula n is the arc length l subtended by the central angle of the circle. The calculation formula is l=nR/180, where R is the radius. ． Core tip: In the arc length formula, l, n, R are known...

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Update Time: 2024-11-18

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 1 industry PPT template

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