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

You are watching: Vertical cross section of a cone

For example, a cylinder-shaped object is cut by a airplane parallel to its base; climate the result cross-section will certainly be a circle. So, there has actually been one intersection that the object. It is not essential that the object needs to be three-dimensional shape; instead, this concept is also applied for 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 shows a ring shape. If we reduced a cubical crate by a plane parallel to its base, then we attain 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 hard by a plane. The cross-section that three-dimensional form is a two-dimensional geometric shape. In other words, the shape obtained by cut a solid parallel come the base is recognized as a cross-section.

Cross-section Examples

The instances for cross-section because that some shapes are:

Any cross-section the the ball is a circleThe vertical cross-section of a cone is a triangle, and also the horizontal cross-section is a circleThe vertical cross-section of 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 overcome Section

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

Vertical or Perpendicular cross Section

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

Cross-sections in Geometry

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

Cross-Sectional Area

When a aircraft cuts a hard object, an area is projected onto the plane. That airplane is then perpendicular to the axis of symmetry. Its projection is well-known as the cross-sectional area.

Example: find the cross-sectional area the a aircraft perpendicular to the basic of a cube the volume equal to 27 cm3.

Solution: due to the fact that we know, 

Volume that cube = Side3

Therefore,

Side3 = 27

Side = 3 cm

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

Cross part of Cone

A cone is considered a pyramid with a circular cross-section. Depending upon the relationship between the aircraft and the slant surface, the cross-section or likewise called conic sections (for a cone) could be a circle, a parabola, one ellipse or a hyperbola.

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

Also, see: Conic Sections course 11

Cross sections of cylinder

Depending on how it has actually been cut, the cross-section the a cylinder might be one of two people circle, rectangle, or oval. If the cylinder has a horizontal cross-section, then the shape derived is a circle. If the plane cuts the cylinder perpendicular to the base, then the shape derived is a rectangle. The oval shape is obtained when the aircraft cuts the cylinder parallel come the base through slight sport in that is angle

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Cross sections of Sphere

We recognize that of all the shapes, a sphere has the smallest surface area because that its volume. The intersection of a aircraft figure with a sphere is a circle. Every cross-sections the a sphere room circles.

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In the over figure, we deserve to see, if a aircraft cuts the round at various angles, the cross-sections we obtain are one only.

Articles on Solids

Solved Problem

Problem: 

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

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Solution:

Given:

Radius = 4 cm

Height = 25 cm

We understand that once the airplane cuts the cylinder parallel to the base, climate the cross-section obtained is a circle.