1, in a cube with side length a, the side with distance a * * * is in a straight line with AD.
a，2 B，3 C，4 D，5
2. The side PAB of the regular pyramid P-ABCD is an equilateral triangle, e is the midpoint of PC, and the cosine of the angle formed by the non-planar straight line BE and PA is
A, B, C, D,
3. If there is a dihedral angle -l- of 1200 and two straight lines a,b,a⊥,b⊥, then the angle formed by ab is equal to
a，300 B，600 C，450 D， 1200
4. If the volume of a regular tetrahedron is 18cm3, the side length of the tetrahedron is
a，6cm B，6cm C， 12cm D，3cm 5。 If the oblique line L forms an angle with the plane and the inner side is the L-plane straight line A, the angle formed by L and A is as follows.
A, max, min b, max, min
C, maximum, minimum d, there is no maximum and minimum.
6. As shown in the figure, in the straight parallelepiped ABCD-A1B1C1D1where ∠BAD=600, diagonal line A1C/Kloc-0.
A, B, C, D,
7. Two planes parallel to the bottom of the cone divide the height of the cone into three equal parts, so the volume ratio of the three parts into which the cone is divided is
a、 1 :2 :3 B、4 :9 :27 C、 1 :7 : 19 D、3 :4 :5
8. The sides of a parallelepiped are all A, and every three sides form an angle of 600 from a vertex, so the volume of the parallelepiped is A, a3 B, C, D,
9. The sides Pa, Pb and PC of the triangular pyramid P-ABC are perpendicular to each other, and the side lengths are 6, 4 and 3 respectively, so the volume of the triangular pyramid is
a，4 B，6 C，8 D， 10
10, the bottom circumference of a regular hexagonal cone is 6 and its height is 0, so its side area is 0.
a，B，6 C，4 D，
1 1, each face of an octahedron is a regular triangle, and one end of each vertex has four sides, so the values of the number of vertices v and the number of edges e should be
a，V=6，E= 12 B，V= 12，E=6 C，V=8，E= 14 D，V= 10，E= 16
Second, fill in the blanks:
1, there are two points in the latitude circle of 450 north latitude, m is at 200 east longitude and n is at 700 west longitude. If the radius of the earth is r, the spherical distance between two points m and n is.
2. There are three points A, B and C on the sphere with radius of 1. It is known that the spherical distances of A and B, A and C are all zero, and the spherical distances of B and C are zero, so the distance from the section passing through A, B and C to the center of the sphere is zero.
3. If all the faces of a simple polyhedron are quadrilateral, then the relationship between the number of vertices v and the number of faces f is.
4. When the radius ratio of three balls is 1 :2 :3, the volume of the largest ball is twice that of the other two balls, and the surface area of the largest ball is twice that of the other two balls.
5. The angle formed by a diagonal of a cuboid and two of the three faces intersecting the same vertex is 300, so the angle formed by it and the other face is.
6. If the three side lengths A, B and C of a cuboid are arithmetic progression, the diagonal length is, and the surface area is 22, then the volume is =.
7. In the triangular pyramid S-ABC, where SA=3, SB=4, SC=4 and SA, SA and SC are perpendicular to each other, the distance from S to the plane ABC is.
8. The lengths of three sides of a cuboid are AA' = 2, AB = 3 and AD = 4, respectively. The shortest distance from point a to c' through the surface of a cuboid is.
9. There are two parallel parts in the center of the sphere, which are 9 cm apart, with an area of 49 square centimeters and 400 square centimeters respectively. If the center of the sphere is not between the two parts, the surface area of the sphere is between the two parts.
10, if all six faces of a parallelepiped are diamonds with a side length of 2 and an acute angle of 600, then its volume is.
Third, answer questions:
1, as shown in the figure, it is known that the height of the quadrangle V-ABCD is h, the bottom surface is rhombic, the angle formed by the side surface VDA and the side surface VDC is 1200, and both are perpendicular to the bottom surface, and the angle formed by the other two sides and the bottom surface is 450, so the total area of the quadrangle can be found.
2. In the oblique triangular prism A'b'c-ABC, the length of each side is a, A'b = A'c = A,
(1) Verification: the side BCC'B is rectangular; (2) Find the distance from B to A side.
3. As shown in the figure, it is known that the side length of the bottom surface of the regular quadrangular prism ABCD-A1B1D1is 3 and the side length is 4. Even if CD 1 is C 1M⊥CD 1, the dihedral angle C 1-A 1m-D 1 is found at m (2).
4. It is known that in the oblique prism ABC-A1B1C1D1,AC=BC, D is the midpoint of AB, the plane ABC⊥ plane ABB 1A, and the straight line BC 1.
(1) verification: ab1⊥ CD; (2) Verification: AB 1⊥ Aircraft A 1CD
(3) if the distance between C 1C and ABB 1A 1 is 1, A 1C=, AB 1=5, find the volume of the triangular pyramid A 1-ACD.
5. In the right-angle prism ABCD-A1B1C1D1,the bottom ABCD is trapezoidal AB//CD, and AB = AD = 2, ∠ BAD = 600, CD =, AA/Kloc. (2) Find dihedral angle b1-ad1-b. 。