"Side expansion diagram of right prism and cone" PPT download

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"Side expansion diagram of right prism and cone" PPT download

Part One Content: Learning Objectives:

1. Understand the side expansion diagrams of right prisms and cones, and further develop the concept of space

2. Be able to use the knowledge of side expansion diagrams of right prisms and cylinders to solve practical problems.

observe

Observe the following three-dimensional figures. They are all right prism objects. Think about what characteristics their shapes have in common?

In geometry, we call the above three-dimensional figure a right prism, where "edge" refers to the common side of two faces.

It has the following characteristics:

(1) There are two surfaces parallel to each other, and they are called bottom surfaces;

(2) The remaining faces are all rectangles, and they are called sides;

(3) The side edge (referring to the common edge of the two sides) is perpendicular to the bottom surface.

Side expansion diagram of right prism and cone PPT, part 2 content: Observation and thinking:

As shown in the figure, a hexagonal prism with a regular hexagonal base is expanded along one of its side edges to obtain the side expansion view of the hexagonal prism.

think:

1. In the picture above, the side expansion of a hexagonal prism is a rectangle. What is the relationship between the length and width of this rectangle and the circumference of the base of the prism and the length of the side edges respectively?

2. As shown in the figure, is the side expansion of a prism with a polygonal base a rectangle? If it is a rectangle, what is the relationship between its length and width and the perimeter and side length of the prism base respectively?

Conclusion: The side expansion view of a right prism is a rectangle, the length of the rectangle is the perimeter of the base of the right prism, and the width of the rectangle is the length of the side edges of the right prism.

Side expansion diagram of right prism and cone PPT, the third part: analysis of examples

Example 1: The side view of a food packaging box is shown in the figure. The bottom surface of the box is a regular hexagon with side length 2. What shape is this packaging box? Try to find its side area based on known data.

Solution: The shape of the packaging box is a hexagonal prism.

Its base circumference is 2×6=12,

Therefore its side area is 12×6=72.

Track training:

1. Among the following geometric figures, which one is a right prism.

2. Among the figures below, the side view of a triangular prism is ()

Analysis: The side expansion view of a prism is a rectangle, and the side expansion view of a triangular prism is three rectangles. Therefore, choose A.

Example 2: (Example question on page 107 of the textbook) As shown in the figure, a cube is shown. Draw a surface expansion diagram of it according to its edges.

Solution: There are many ways to expand by edges, one of which is as shown in the figure.

Side expansion diagram of right prism and cone PPT, part 4 content: expansion and improvement:

1. As shown in the picture, there is a cube-shaped room with a side length of 4 meters. A spider is at A and a fly is at B.

⑴What is the shortest distance a spider needs to crawl to catch a fly?

⑵If the fly is at C, what is the shortest distance?

2. As shown in the figure, it is known that the length, width and height of a cuboid carton are 30 cm, 20 cm and 10 cm respectively. An insect climbs from the vertex A of the carton to another vertex along the carton surface ACDE and surface GEDB. At B. Which route does it crawl along for the shortest distance? Please explain the reason and find the shortest distance.

think:

1. How many ways can a cuboid be expanded so that point A and point B are on the same plane?

2. How to find the shortest distance between two points on the same plane?

3. Among the expanded diagrams of a cuboid, which expanded diagram has the shortest distance between points A and B?

Side expansion diagram of right prism and cone PPT, part 5 content: knowledge summary

1. Three-dimensional figures are surrounded by faces. If the same three-dimensional figure is expanded in different ways, the resulting plane figures will be different.

2. The side expansion view of a cone is a fan shape.

The side expansion view of a cone is a fan shape. The radius of the fan shape is the length of the generatrix of the enclosed cone, and the arc length of the fan shape is the circumference of the base of the enclosed cone.

On-site training

1. As shown in the figure is an expanded view of a cube carton. After the expanded view is folded into a cube along the dotted line, the two numbers on the opposite surfaces are opposite to each other. Find:

2. As shown in the figure, the side expansion view of a cone is a semicircle.

Find the angle between bus AB and high AO;

3. If the generatrix length of the cone is 5 cm and the base radius is 3 cm, then the total area of ​​the cone is 24π cm2.

Analysis: The side area of ​​the cone is 1/2×5×(3×2×π)=15π(cm2), and the base area is π×32=9π(cm2), so the total area of ​​the cone is 15π+9π=24π( cm2). So fill in 24π cm2.

Keywords: Free download of mathematics PPT courseware for the second volume of the ninth grade of the Hebei Education Edition, PPT download of side expansion diagrams of right prisms and cones, .PPT format;

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Update Time: 2024-06-14

This template belongs to Mathematics courseware Hebei Education Edition Ninth Grade Mathematics Volume 2 industry PPT template

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