Cross section means the representation of the intersection of an item by a aircraft along that 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: Perpendicular cross section of a cylinder

For example, a cylinder-shaped object is reduced by a plane parallel to its base; climate the result cross-section will be a circle. So, there has been an intersection that the object. That is not vital that the object has to be three-dimensional shape; instead, this principle is additionally applied because that two-dimensional shapes.

Also, you will see some real-life examples of cross-sections such together a tree after it has actually been cut, which reflects a ring shape. If we reduced a cubical crate by a plane parallel to its base, climate 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 solid by a plane. The cross-section that three-dimensional shape is a two-dimensional geometric shape. In various other words, the shape obtained by cutting a solid parallel come the base is well-known as a cross-section.

Cross-section Examples

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

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

Types of overcome Section

The cross-section is of two types, namely

Horizontal cross-sectionVertical cross-section

Horizontal or Parallel overcome Section

In parallel cross-section, a aircraft cuts the solid shape in the horizontal direction (i.e., parallel come the base) such that it creates 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 cross sectional area of different solids is provided here through examples. Allow us number out the cross-sections that cube, sphere, cone and also cylinder here.

Cross-Sectional Area

When a aircraft cuts a hard object, one area is projected top top the plane. That airplane is climate perpendicular to the axis the symmetry. Its forecast is recognized as the cross-sectional area.

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

Solution: because we know, 

Volume the cube = Side3

Therefore,

Side3 = 27

Side = 3 cm

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

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

Volume by cross Section

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

Cross sections of Cone

A cone is thought about a pyramid through a one cross-section. Depending upon the relationship between the plane and the slant surface, the cross-section or additionally called conic sections (for a cone) might be a circle, a parabola, an ellipse or a hyperbola.

*

From the above figure, we have the right to see the different cross sections of cone, as soon as a airplane cuts the cone in ~ a various angle.

Also, see: Conic Sections class 11

Cross part of cylinder

Depending on just how it has been cut, the cross-section of 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 acquired is a rectangle. The oval form is obtained when the aircraft cuts the cylinder parallel come the base v slight sports in that angle

*

Cross sections of Sphere

We recognize that of every the shapes, a sphere has actually the smallest surface area because that its volume. The intersection the a aircraft figure v a sphere is a circle. All cross-sections that a sphere space circles.

*

In the over figure, we can see, if a airplane cuts the round at various angles, the cross-sections we gain are circles only.

Articles top top Solids

Solved Problem

Problem: 

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

See more: What Are The Similarities Between Hinduism And Buddhism And Hinduism

Solution:

Given:

Radius = 4 cm

Height = 25 cm

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