Knowledge and skills: Understand the geometric characteristics of cylinders, cones, platforms and spheres, draw three views and straight views, and calculate the surface area and volume.
Process and method: Through the formation of the rotating body, master the method of using the axis cutting space problem as a plane problem. Can draw, read and use pictures.
Emotional attitude and values: cultivate practical ability and spatial imagination ability, from appreciating the beauty of graphics to discovering and creating beauty.
Second, learning is arduous and difficult.
Learning focus: the characteristics of each space geometry, the calculation formula and drawing method of space graphics.
Learning difficulties: the establishment of spatial imagination ability, the recognition and application of spatial graphics.
3. Instructions for use and guidance in learning: Combining the definition of spatial geometry, observe the graphics of spatial geometry, and cultivate the ability of spatial imagination, memorizing formulas and flexible application.
Fourth, knowledge link 1. Recall the geometric features of cylinders, cones, platforms and spheres. 2. Remember the formulas of surface area and volume.
Verb (abbreviation of verb) learning process
Question 1: Basic concept problem
Example A 1: (1) The following statement is incorrect ()
A: The lateral expansion of the cylinder is a rectangle. B: The axial section of the cone is an isosceles triangle. C: The geometric figure surrounded by the curved surface formed by the right triangle rotating around one side is a cone. D: The section of the frustum parallel to the bottom is a circular surface.
(2) The following statements are correct: (a) The bottom of a prism must be a parallelogram; B) The bottom of the pyramid must be a triangle; C) Two parts of a pyramid divided by a plane cannot both be pyramids; D) Both parts of the prism divided by the plane can be prisms.
Question 2: Three Views and Intuitive Questions
B Example 2: The figure below is three views of a geometry, which should be a ().
A prism, B pyramid, C prism and D are all wrong.
B Example 3: A triangle corresponds to a regular triangle with a side length of 1 in its orthographic drawing, and the area of the original triangle is ().
A.B. C. D。
Question 3: Calculation of surface area and volume.
Example 4: It is known that the height of the regular four columns whose vertices are on a sphere is 4 and the volume is 16, so the surface area of this sphere is ().
In the 1932 s BC,
C Example 5: If the side length of a cube is, the volume of a convex polyhedron with the center of each face of the cube as the vertex is ().
(A) (B) (C) (D)
Question 4: About combination.
Example 6: Three views of known geometry are as follows. According to the dimension (unit: cm) marked in the drawing, the volume of this geometry can be obtained as ().
A.B. C. D。
Sixth, standardize training.
1. If all three views of a geometry are isosceles triangles, the geometry may be ().
A. Cone B. Regular quadrangular pyramid C. Regular triangular pyramid D. Regular triangular pyramid
2, a trapezoid with oblique drawing method to make its vertical diagram, the vertical diagram area is the original trapezoid area ().
A times b times c times d times
3. Cut a circular piece of paper into two sectors along the radius, and the ratio of central angles is 3: 4. Then roll them into two conical sides.
Surface, the volume ratio of two cones is ()
A.3: 4 b.9:16 c.27: 64 d. are all wrong.
4. It is obtained by oblique two-pulling method.
① The orthographic drawing of a triangle must be a triangle; ② The orthogonal projection of a square must be a diamond;
③ Isometric view of isosceles trapezoid can be parallelogram; ④ The orthographic projection of the rhombus must be a rhombus.
The above conclusion is correct ()
A.①② B. ① C.③④ D. ①②③④
5. There is a three-view geometry as shown in the figure below. This geometry should be ().
A prism, B pyramid, C prism and D are all wrong.
6. If the three views of a geometric figure are as shown in the figure, the front view and the left view are regular triangles with a side length of 2, and the outline of the top view is square (unit length: cm), then the lateral area of this geometric figure is ().
A. centimeter square centimeter
C.12cm diameter14cm2
7. If the surface area of a cone is square meters and its side is unfolded into a semicircle, the diameter of the bottom surface of the cone is
8. Take a sector with a central angle of and an area of as the side of the cone, and find the surface area and volume of the cone.
9. As shown in the figure, in quadrilateral,,,, find the surface area and volume of the geometry formed by one rotation of quadrilateral.
10, (as shown in the figure) A tall cylinder is inscribed on a cone with a base radius of 2 and a generatrix length of 4, and the surface area of the cylinder is calculated.
Seven. Summary and reflection
There is no knowledge that cannot be learned, only students that cannot be learned.
Summary: 20 13 has arrived, and the new year's Mathematics Network will also collect more and better articles for you. I hope this math teaching plan: space geometry can help you!