Question

how many different types of cross sections of a cone are possible?

3
5
6
10

Explanation:

Identify possible cross sections of a cone

• Circle (plane parallel to the base, not passing through the apex)
• Ellipse (plane tilted relative to the base, cutting through all lateral edges)
• Parabola (plane parallel to a generator line of the cone)
• Hyperbola (plane cutting both halves of a double cone, or a single branch on a single cone)
• Triangle (plane passing vertically through the apex)
• Point (plane intersecting only the apex)

Count the unique geometric shapes

$$ N = 6 \quad (\text{Circle, Ellipse, Parabola, Hyperbola, Triangle, Point}) $$

Answer:

• 3
• 5
• 6 (Correct answer)
• 10