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.
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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 circleTypes of overcome Section
The cross-section is of two types, namely
Horizontal cross-sectionVertical cross-sectionHorizontal 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.
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Solved Problem
Problem:
Determine the cross-section area that the offered cylinder whose height is 25 cm and also radius is 4 cm.
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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.