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Solving problems in solid geometry of senior two mathematics.
1. In the cube AC', m and n are the midpoint of AA'BB' respectively. What is the length of the positive rotation value D'N of the angle formed by the straight line CM and D'N?

The length of D'N must be required, and the side length must be known first.

Then connect your D'B so that D'B'N is a right triangle.

Assuming the side length is 1, it is easy to conclude that B'D' is the "root number 2" in the bottom surface A'B'C'D'. Then n is the midpoint. B'N is "half"

Then there is Pythagorean theorem. D'N equals NB' plus B'D'.

2. 1. As we all know, the volume of a ball is equal to the volume of a cube. Compare the surface areas of spheres and cubes.

4/3*πr^3 = a^3->; A = (4/3 * π) (1/3) * r, s sphere = 4 * π r 2, s square = 6 * A 2,

3. It is known that the points P, PA⊥ plane ABCD, E and F outside the rectangular ABCD plane are the midpoint of AB and PC respectively. Verification: EF⊥CD.

Connect AC, where the point is G, the projection of F on ABCD is G, EG is the projection of EF on ABCD, and EG is perpendicular to DC, so EF is perpendicular to DC.

The length of each side of a parallelepiped is 4. On the three sides starting from the vertex P, take PA= 1, PB=2 and PC=3 respectively, and the volume of the pyramid P-ABC is several times that of the original parallelepiped.

If the triangle PAB is the base, S is the parallelepiped 1/2*`4* 1/2.

When the height is 3/4 times of the original height, the volume is multiplied by 1/3 and 1/64.

5. Let the vertices A and B of △ABC be out of plane α, and the vertex C be in plane α. The projection of AB on α is A 1, B 1, AA 1 < BB 1, and the height of △ABC on the BC side is AD, forming an AD‖ plane α, BC, α.

AD is perpendicular to BC, and AD || A A, B, C and D are coplanar. The answer is the angle formed by BC and a.

6. It is known that straight lines A and B are non-planar straight lines, and straight line C is parallel to A and C and B do not intersect. Prove that b and c are non-planar straight lines.

Reduction to absurdity. If b and c are not straight lines on different planes, and because b and c do not intersect, b and c are parallel.

And because A and C are parallel, A and B are also parallel.

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