Cross section of a Cone
A cross section is a representation of an intersection of a shape with a plane along its axis of symmetry. When a solid, such as a cone, cylinder, or sphere, is cut by a plane, it produces a shape called a cross-section. The cross-section of a solid such as a cone can be a circle, a parabola, or a triangle depending on the manner in which the plane cuts the cone.
Different Cross-sections of a Cone
- A cross section of a cone is circular when it is cut horizontally.
- Cross-section of a cone is an isosceles triangular when it is cut vertically and this plane cuts through the center of the cone.
- Cross-section of a cone is parabolic when it is cut vertically with the exception of the plane passing through the center.
Solved Examples
Example 1: What cross-sections are produced when an ice cream cone is cut by a plane?
Solution:
When a plane cuts an ice cream cone, we get the following types of cross sections:
Vertical cut: Two triangular-shaped pieces are obtained.
Horizontal cut: One tiny cone and a frustum, the remaining part of the cone without the tip, is obtained.
Example 2: What cross sections are produced when a traffic cone is cut?
Solution:
When we cut a traffic cone, we get the following cross section:
Vertical cut: Two triangular-shaped pieces are obtained.
Horizontal cut: One tiny cone and a frustum are produced.
The shapes of the cross-sections of a cone are an isosceles triangle, a parabola or a circle.
The lower part of a cone when it is sliced about the axis parallel to its base, is called the frustum of a cone.
A Christmas tree, ice cream cones, party hats, funnels, and traffic cones are a few common examples of cone shaped objects.