Cross section means the representation the the intersection of an object by a airplane along its axis. A cross-section is a form that is surrendered from a solid (eg. Cone, cylinder, sphere) when reduced by a plane.
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For example, a cylinder-shaped object is reduced 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. That is not necessary that the object has to be three-dimensional shape; instead, this concept is also applied for two-dimensional shapes.
Also, you will view some real-life instances of cross-sections such as a tree ~ it has actually been cut, which shows a ring shape. If we reduced a cubical box by a plane parallel come its base, then we obtain a square.
| Table that contents:Types of overcome section |
Cross-section Definition
In Geometry, the cross-section is identified as the shape acquired 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 derived by cutting a hard parallel come the basic is recognized as a cross-section.
Cross-section Examples
The instances for cross-section because that some shapes are:
Any cross-section of the round is a circleThe upright cross-section that a cone is a triangle, and the horizontal cross-section is a circleThe upright cross-section that a cylinder is a rectangle, and 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 cross Section
In parallel cross-section, a airplane cuts the solid form in the horizontal direction (i.e., parallel come the base) such the it creates the parallel cross-section
Vertical or Perpendicular overcome Section
In perpendicular cross-section, a airplane cuts the solid shape in the vertical direction (i.e., perpendicular come the base) such that it creates a perpendicular cross-section
Cross-sections in Geometry
The overcome sectional area of various solids is given here through examples. Let us number out the cross-sections the cube, sphere, cone and cylinder here.
Cross-Sectional Area
When a aircraft cuts a solid object, one area is projected onto the plane. That aircraft is climate perpendicular come the axis the symmetry. Its projection is well-known as the cross-sectional area.
Example: find the cross-sectional area that a aircraft perpendicular come the basic of a cube the volume same 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 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 ar of a solid is a two-dimensional shape, therefore, us cannot recognize its volume.
Cross sections of Cone
A cone is considered a pyramid with a one cross-section. Depending on the relationship in between the plane and the slant surface, the cross-section or also called conic sections (for a cone) could be a circle, a parabola, an ellipse or a hyperbola.
From the over figure, we deserve to see the various cross sections of cone, when a airplane cuts the cone in ~ a various angle.
Also, see: Conic Sections class 11
Cross sections of cylinder
Depending on just how it has been cut, the cross-section of a cylinder may 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 airplane cuts the cylinder perpendicular come the base, climate the shape obtained is a rectangle. The oval shape is obtained when the aircraft cuts the cylinder parallel to the base v slight sport in the angle
Cross part of Sphere
We understand that of all the shapes, a sphere has actually the smallest surface ar area for its volume. The intersection the a airplane figure v a ball is a circle. Every cross-sections that a sphere room circles.
In the above figure, we deserve to see, if a plane cuts the round at various angles, the cross-sections we gain are one only.
Articles ~ above Solids
Solved Problem
Problem:
Determine the cross-section area of the offered 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 once the plane cuts the cylinder parallel come the base, then the cross-section acquired is a circle.