In geometry, we study about shapes which are usually predefined geometrical figures. Sometimes, one needs to study about the cross section of a shape. The Cross section is one of the important concepts in mathematics. It is defined as the two-dimensional plane obtained by the intersection of a three-dimensional solid shape with the help of a plane. It is quite obvious that cross sectioned surface of a three-dimensional object is a two-dimensional shape.
There are two types of cross sections -
(1) Horizontal Cross Section
(2) Vertical Cross Section
A horizontal cross section is obtained when the plane that passes through the solid object is parallel to its base. On the other hand, a vertical cross section is found when the intersecting plane is perpendicular to the base of the solid. These are known as parallel cross section and perpendicular cross section.
The cross section is the section of the figure after cutting it. For example -
(1) Any cross section of a sphere is a circle.
(2) A horizontal cross section of a cone is a circle, while its vertical cross section is a triangle.
(3) The horizontal cross section of a cylinder is circle and the vertical cross section is a rectangle.
In this article, we are going to learn about definition of cross sections with suitable problems and figures and their applications.
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In geometry the shape obtained by the intersection of a solid by a plane is called as Cross-section. This cross section is mainly happened only on three dimensional geometrical shapes like Rectangular prism, pyramid, triangular prism, pyramid and cube.
For example: Cross section of a sphere is circle.
Definition of Parallel cross section: A plane bisects the solid object in the direction of horizontal that creates the parallel cross section. In the below figure 1 represents the Rectangular prism solid object that can be cut by the plane through the horizontal direction that is parallel. This is outlined as the parallel cross section.Definition of Perpendicular cross section (vertical cross section): A plane bisects the solid object in the direction of vertical that creates the perpendicular cross section. In the below figure 2 represents the Rectangular prism solid object that can be cut by the plane through the vertical direction that is perpendicular. This is outlined as the perpendicular cross section.
Below are the examples on Cross Section -
See the below diagram and then find the type of the cross section and identify the part of the parallel cross section
Solution: Here the given diagram looks like as the pentagonal prism. This solid is uniformly cut by the plane and it’s parallel to the base. So it is comes under the type of the parallel cross section. This cross section is same to the figure 2. Because the original figure of the parallel cross section of pentagonal prism is the pentagon.
Which is the cross section of the given rectangular prism, after cutting vertically?
Solution:A is correct (because cross section of the given figure is a rectangle).Problem 3: Find the area of cross section of the given figure. Solution: From the given figure: Cross section of the figure is rectangular.
So the area of the cross section = Length * Width
= 5m * 3m
= 15 m2
Therefore, the area of cross section is 15 m2.
Solution:The cross section area of a cylinder after cutting it vertically is a circle.The area of a circle = $\pi$r2So area of cross section is = 3.14 * 52 cm2
= 3.14 * 25 cm2
= 75.5 cm2Thus the cross section area of the cylinder is 75.5 cm2.
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