Cross section means the representation that the intersection of an object by a plane along its axis. A cross-section is a form that is surrendered from a heavy (eg. Cone, cylinder, sphere) when cut by a plane.

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For example, a cylinder-shaped thing is cut by a airplane parallel to its base; climate the result cross-section will be a circle. So, there has actually been an intersection of the object. The is not vital that the object has to be three-dimensional shape; instead, this principle is additionally applied for two-dimensional shapes.

Also, you will watch some real-life examples of cross-sections such as a tree ~ it has been cut, which shows a ring shape. If we cut a cubical crate by a airplane parallel to its base, then we obtain a square.

Table that contents:Types of cross section

Cross-section Definition

In Geometry, the cross-section is characterized as the shape derived by the intersection of heavy by a plane. The cross-section that three-dimensional form is a two-dimensional geometric shape. In various other words, the shape obtained by cut a hard parallel come the base is recognized as a cross-section.

Cross-section Examples

The examples for cross-section for some shapes are:

Any cross-section the the ball is a circleThe vertical cross-section that a cone is a triangle, and also the horizontal cross-section is a circleThe vertical cross-section the a cylinder is a rectangle, and also the horizontal cross-section is a circle

Types of overcome Section

The cross-section is of 2 types, namely

Horizontal cross-sectionVertical cross-section

Horizontal or Parallel cross Section

In parallel cross-section, a plane cuts the solid shape in the horizontal direction (i.e., parallel to the base) such that it create the parallel cross-section

Vertical or Perpendicular overcome Section

In perpendicular cross-section, a plane cuts the solid form in the vertical direction (i.e., perpendicular come the base) such the it creates a perpendicular cross-section

Cross-sections in Geometry

The overcome sectional area of different solids is provided here with examples. Allow us figure out the cross-sections of cube, sphere, cone and cylinder here.

Cross-Sectional Area

When a plane cuts a heavy object, one area is projected top top the plane. That airplane is then perpendicular come the axis of symmetry. Its projection is well-known as the cross-sectional area.

Example: uncover the cross-sectional area that a plane perpendicular come the basic of a cube of volume equal to 27 cm3.

Solution: because we know, 

Volume the cube = Side3


Side3 = 27

Side = 3 cm

Since, the cross-section the the cube will be a square therefore, the next of the square is 3cm.

Hence, cross-sectional area = a2 = 32 9

Volume by cross Section

Since the cross ar of a heavy is a two-dimensional shape, therefore, us cannot recognize its volume. 

Cross part of Cone

A cone is thought about a pyramid v a one cross-section. Relying on the relationship between the aircraft and the slant surface, the cross-section or likewise called conic sections (for a cone) might be a circle, a parabola, one ellipse or a hyperbola.


From the over figure, we deserve to see the different cross sections of cone, as soon as a plane cuts the cone in ~ a different angle.

Also, see: Conic Sections class 11

Cross sections of cylinder

Depending on just how it has been cut, the cross-section the a cylinder may be either circle, rectangle, or oval. If the cylinder has a horizontal cross-section, climate the shape obtained is a circle. If the plane cuts the cylinder perpendicular to the base, then the shape obtained is a rectangle. The oval form is derived when the plane cuts the cylinder parallel to the base through slight sports in the angle


Cross sections of Sphere

We know that of every the shapes, a sphere has the smallest surface area for its volume. The intersection that a plane figure through a sphere is a circle. Every cross-sections the a sphere space circles.


In the above figure, we deserve to see, if a aircraft cuts the round at various angles, the cross-sections we acquire are circles only.

Articles ~ above Solids

Solved Problem


Determine the cross-section area that the provided cylinder whose elevation is 25 cm and also radius is 4 cm.

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Radius = 4 cm

Height = 25 cm

We recognize that as soon as the plane cuts the cylinder parallel to the base, climate the cross-section acquired is a circle.