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

Therefore,

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 sq.cm.

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.

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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

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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.

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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

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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Solution:

Given:

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.