Cross section means the representation the the intersection of an item by a airplane along its axis. A cross-section is a shape that is succumbed from a hard (eg. Cone, cylinder, sphere) when reduced by a plane.

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For example, a cylinder-shaped object is cut by a plane parallel to its base; then the result cross-section will certainly be a circle. So, there has actually been one intersection of the object. The is not crucial that the object needs to be three-dimensional shape; instead, this concept is also applied because that two-dimensional shapes.

Also, friend will check out some real-life examples of cross-sections such together a tree ~ it has actually been cut, which mirrors a ring shape. If we reduced a cubical box by a airplane parallel to its base, then we acquire a square.


Table of contents:Types of overcome section

Cross-section Definition

In Geometry, the cross-section is defined as the shape derived by the intersection of hard 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 basic is recognized as a cross-section.

Cross-section Examples

The examples for cross-section for some shapes are:

Any cross-section that the sphere is a circleThe upright cross-section the a cone is a triangle, and the horizontal cross-section is a circleThe upright cross-section the a cylinder is a rectangle, and the horizontal cross-section is a circle

Types of cross Section

The cross-section is of two types, namely

Horizontal cross-sectionVertical cross-section

Horizontal or Parallel cross Section

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

Vertical or Perpendicular overcome Section

In perpendicular cross-section, a aircraft cuts the solid shape in the upright direction (i.e., perpendicular to the base) such the it create a perpendicular cross-section

Cross-sections in Geometry

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

Cross-Sectional Area

When a aircraft cuts a solid object, one area is projected ~ above the plane. That aircraft is then perpendicular come the axis that symmetry. Its projection is known as the cross-sectional area.

Example: find the cross-sectional area that a airplane perpendicular come the basic of a cube that volume same to 27 cm3.

Solution: due to the fact that we know, 

Volume the cube = Side3

Therefore,

Side3 = 27

Side = 3 cm

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

Hence, cross-sectional area = a2 = 32 9 sq.cm.

Volume by overcome Section

Since the cross section of a hard is a two-dimensional shape, therefore, we cannot identify its volume. 

Cross sections of Cone

A cone is thought about a pyramid with a circular cross-section. Depending upon the relationship between the airplane and the slant surface, the cross-section or also called conic part (for a cone) might be a circle, a parabola, an ellipse or a hyperbola.

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From the above figure, we deserve to see the different cross part of cone, once a aircraft cuts the cone in ~ a various angle.

Also, see: Conic Sections course 11

Cross part of cylinder

Depending on how it has been cut, the cross-section of a cylinder might be either circle, rectangle, or oval. If the cylinder has actually a horizontal cross-section, climate the shape obtained is a circle. If the plane cuts the cylinder perpendicular to the base, then the shape acquired is a rectangle. The oval form is acquired when the aircraft cuts the cylinder parallel come the base v slight variation in that angle

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Cross part of Sphere

We recognize that of every the shapes, a sphere has the smallest surface area for its volume. The intersection that a airplane figure v a ball is a circle. All cross-sections of a sphere room circles.

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In the above figure, we deserve to see, if a airplane cuts the ball at different angles, the cross-sections we gain are one only.

Articles ~ above Solids

Solved Problem

Problem: 

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

See more: Earth Has No Sorrow That Heaven Cannot Heal Scripture, There Is No Sorrow That Heaven Cannot Heal

Solution:

Given:

Radius = 4 cm

Height = 25 cm

We recognize that once the plane cuts the cylinder parallel come the base, then the cross-section derived is a circle.