First, multiple-choice questions (5 points for each question, ***35 points)
1. Of the following four figures, the one that is the plane expansion diagram of triangular prism is (b).
A B C D
2. In the following geometry, (c) is a triangle when viewed from the front.
A B C D
Analysis: a. The front view is rectangular; B. The front view is rectangular; C. The front view is triangular; D. The front view is square with a line in the middle, so C is chosen.
3. The surface development diagram of a cube is shown in the figure. There is a word on each of the six faces, which means "I wish the entrance examination a success". After being folded into a cube, the word opposite to "Cheng" is (b).
A. Medium B. Work
C. Test D. Wish
Analysis: This is a flat expansion diagram of a cube. * * * has six faces, among which "Cheng" is opposite to "Gong", "Qian" is opposite to "Zhu" and "Zhong" is opposite to "Kao", so choose B.
4. As shown in the figure, five identical cubes are combined into a three-dimensional figure, and the figure seen from its left is (B).
A B C D
5. In the following geometry, there is one geometry, and the shape diagram seen from it is different from the other three. This geometry is (a).
6. As shown in the figure, it is a geometric figure obtained after one corner of the cube is cut off. Seen from above, its shape diagram is (A).
7. As shown in the figure, a geometric figure composed of the same small cubes is seen from above, and the numbers in the small squares indicate the number of small cubes in this position, so the geometric figure seen from the left is (B).
Fill in the blanks (4 points for each question, 24 points for * * *)
8. As shown in the figure, a small square is added to the plan, so that the figure can be folded into a quadrangular prism. There are four different ways to add * * *.
9. If the graph is an expanded graph of a cube, the minimum value of the sum of the numbers of the original cube relative to the two faces is 6.
10. A prism has 12 vertices and the sum of all sides is 30 cm, so the length of each side is 5cm.
1 1. As shown in the figure, the figure rotates once along the dotted line, and the closed geometry is a cylinder.
12. Geometry is composed of several small cubes with the same size. When you look at this geometry from above, the shape diagram is as shown. The number in the small square indicates the number of small cubes in this position. If you look at this geometry from the front, you can see six cubes.
13. The side spread of the cone is a semicircle, as shown in the figure, so its surface area is 27πcm2.
Iii. Solving problems (***4 1 point)
14.( 12 minutes) As shown in the figure, cut off a small square in the figure so that the rest can be folded into cubes. Which small square should I cut off?
Solution: cut out the building, either beautiful or beautiful.
15.( 14 minutes) As shown in the figure, a three-dimensional figure composed of several identical cubes is viewed from three different directions. Answer the following questions according to the shape diagram:
(1) How many layers did the original stereogram * * * have?
(2) How many small cubes are there in the three-dimensional graph?
Solution: (1) two layers; (2) five.
16.( 15 minutes) As shown in the figure, the faces of a cuboid are unfolded, and letters are marked on each face (letters are outward). Answer the following questions:
(1) If you put face A at the bottom of a cuboid, which face will be on it?
(2) If the F surface is in front, which side will be on the B surface when viewed from the left?
(3) From the right, it's face C, and the left is face E, so which face will be on it?
Solution: (1) plane f; (2) curved surface c; (3) surface b or d.