FREE Gaokao Solid Geometry Proofs and Calculations Questions and Answers

Question 1

In the pyramid P-ABCD, the base ABCD is a rectangle.
E is the midpoint of the side PD.
Let plane α be the plane passing through points A, E, and C.
What is the relationship between line PB and plane α?

Accepted Answer

PB is parallel to plane α

Answer

PB lies within plane α

Answer

PB intersects plane α

Answer

The relationship is uncertain

Question 2

In a cube ABCDA'B'C'D' with side length 'a', what is the sine of the angle between the line A'B and the plane BDD'B'?

Accepted Answer

1/2

Answer

√2/2

Answer

√3/3

Answer

√3/2

Question 3

In a triangular pyramid P-ABC, the base ABC is an equilateral triangle with a side length of 2. If PA is perpendicular to the base plane ABC and PA = 3, what is the volume of the pyramid P-ABC?

Accepted Answer

√3

Answer

3√3

Answer

3

Answer

2√3

Question 4

In a regular tetrahedron with an edge length of 3, what is the distance from any vertex to the opposite face?

Accepted Answer

√6

Answer

√3

Answer

2√2

Answer

3√2/2

Question 5

In the right triangular prism ABC-A₁B₁C₁, ∠BCA = 90°, and AC = BC = CC₁ = 1. What is the cosine of the dihedral angle B₁-AC₁-B?

Accepted Answer

2√2/3

Answer

1/3

Answer

√2/2

Answer

√3/3

Question 6

A rectangular box has side lengths of 2, 3, and 6. What is the surface area of the sphere that circumscribes this box?

Accepted Answer

49π

Answer

14π

Answer

24.5π

Answer

196π

In the pyramid P-ABCD, the base ABCD is a rectangle.E is the midpoint of the side PD.Let plane α be the plane passing through points A, E, and C.What is the relationship between line PB and plane α?

In the pyramid P-ABCD, the base ABCD is a rectangle.
E is the midpoint of the side PD.
Let plane α be the plane passing through points A, E, and C.
What is the relationship between line PB and plane α?