Gaokao Exam Solid Geometry Proofs and Calculations 2

Question 1

A regular triangular prism has base edge length 4 and height 6. What is its total surface area?

Accepted Answer

72 + 8√3

Answer

48 + 8√3

Answer

72 + 4√3

Answer

48 + 4√3

Question 2

In a rectangular box (cuboid) with dimensions 3 × 4 × 12, what is the length of the space diagonal?

Accepted Answer

13

Answer

√193

Answer

√169 = 13

Answer

5

Question 3

A sphere is inscribed in a regular tetrahedron with edge length a. Which formula gives the radius of the inscribed sphere?

Accepted Answer

r = a√6/12

Answer

r = a/2

Answer

r = a√3/6

Answer

r = a/4

Question 4

The dihedral angle between two adjacent faces of a regular tetrahedron is approximately:

Accepted Answer

arccos(1/3) ≈ 70.5°

Answer

60°

Answer

90°

Answer

120°

Question 5

A cone has base radius r and slant height l. What is the lateral surface area?

Accepted Answer

πrl

Answer

πr²

Answer

2πrl

Answer

πr²l

Question 6

In the Gaokao solid geometry proof format, what is the standard first step when asked to prove that a line is perpendicular to a plane?

Accepted Answer

Show that the line is perpendicular to two distinct lines within the plane that intersect at a point

Answer

Show that the line is parallel to another perpendicular line

Answer

Measure the angle directly

Answer

Show that the line's projection onto the plane is a point

A regular triangular prism has base edge length 4 and height 6.What is its total surface area?