Content Curator
Section of solid refers to the sections of an object cut by an imaginary plane in order to highlight the internal angles of the object. Sections of solid can be obtained by various means such as by horizontal plane, vertical plane, auxiliary plane, auxiliary vertical plane and profile plane. In geometry the sections of solids have six types of view which include full sections, half sections, offset sections, broken out sections, revolving sections and removed sections.
| Table of Content |
Key Takeaways: Solid shapes, Shadows, Slicing
Definition of Solid (3D) Shapes
[Click Here for Sample Questions]
Figures are classified in terms of dimension. Around us which have different shapes. Objects or figures having lengths only are known as one dimensional objects. The common in most of the objects that they have some length, breadth, height and depth.
Also Read:
Properties of Solid (3D) Shapes
[Click Here for Sample Questions]
Three dimensional - In three dimensional objects you can see different shapes in the same objects. For example if you see a pyramid from top you can see only a square but when you see it from the side you can see a triangle. Mainly, there are 4 properties of 3D Shapes:
Faces
A flat surface or a curved surface of any solid figure is known as its face. There can be multiple faces in a solid shape. For Example, a cube has 3 faces, whereas a cylinder has 3 faces.
Edges
A place where two faces meet and make a straight line is known as its edge. There can be multiple Edges in a solid shape. For Example, a cube has 12 edges, whereas a cylinder has 2 edges.
Vertices
A corner where the edges of the solid meet is known as vertex. Multiple vertex are known as vertices. For Example, a cube has 8 vertices, whereas a cone has only 1 vertex.
Volume
The total space which can be occupied by a solid figure is known as its volume. Volumes of various figures can be found out by different formulas for different figures.
Also Read:
Cross Section of Solid Shapes
[Click Here for Sample Questions]
A section will show its true shape when viewed in the normal direction. To find the true shape of a section, it must be a projection of the plane parallel to the section plane. The internal hidden details of the object are shown in orthographic views of dashed lines.
Also Read:
Difference between Section and Cross Section
[Click Here for Sample Questions]
A key difference is section refers to the cutting of a solid by or along a plane whereas a cross section is to the surface or the shape that is exposed by cutting through it. Section and cross section these two terms are used for design and mathematics. Section is related to a process of cutting a solid; the cut is made along a plane. Cross sectional view is the term related to slicing the object. For example, if you cut the circle in half, how it will look. Every cross sectional view looks rectangular after cutting the bread.
If you cut the cylinder vertical you will get slices of circles. The section is cylinder and cross section is circles.
Viewing Different Sections of Solids
[Click Here for Sample Questions]
There are following ways of viewing different sections of solids:
Cutting or Slicing of 3D Shapes
You can get a net for a cone by cutting a slit along its slant surface in the figure.
An object which is 3D can be viewed in different views, however the original image cannot be retained after cutting or slicing. Hence the cross-section of the 3D objects is present within an object and to view a particular 3D object, one can cut the object either horizontally, vertically or from any angle.
Shadow Play
Shadow play refers to the phenomenon which occurs when a light is focused on an object how it will look. For example if you focus the torch on the sphere from its centre the shadow always looks like a circle. Shadows are a good way to illustrate three dimensional objects that can be viewed in two dimensions. Keep a torchlight right in front of a cone; it will cast shadow in front of the screen.,
Object from certain angles
A third way is by looking at objects from certain angles to get different views. If you see objects from different angles like front view, top view and side view.
Things to Remember
Following are some important points:
- Objects or figures having lengths only are known as one dimensional objects.
- A vertex or vertices is a point where two or more straight lines meet.
- An edge is a line segment that joins two vertices.
- Shadow play is a method to view 3D objects into 2D objects.
- In three dimensional objects you can see different shapes in the same objects.
Also Read:
Sample Questions
Ques: Which cross section will be obtained if the square pyramid shown below is cut vertically away from the top? (2 Marks)
Ans: It will give us trapezium face shape. We get a trapezium cross section of a square pyramid. If we cut one piece from the whole figure, we will get a trapezium as shown in the figure.
Ques: A light source was placed in front of a three dimensional shape. These give a circular shadow. But side light was cast on the three dimensional shape, a rectangular shadow was obtained. Similarly, a rectangular shadow was also obtained when light was from top. Identify the three dimensional shape. (2 Marks)
Ans: A cylinder – top view is that of a rectangle, front view is that of a rectangle and side view is circle. We can see this in the following figure.
Ques: Find the front view, side view and top view of the solid shown. (2 Marks)
Ans: The front view, top view and side view is shown in the figure below.
Thus, we can see that the front, top, and side views of this figure are similar.
Ques: Find the front view, side view and top view of the solid shown. (2 Marks)
Ans: The front view, top view and side view is shown in the figure below.
Ques: Explain the concept of shadow and slicing the object with examples. (3 Marks)
Ans: Following are the concepts:
- Viewing an object is by cutting or slicing: Cross sectional view is the term related to slicing the object. For example, if you cut the circle in half, how it will look. Every cross sectional view looks rectangular after cutting the bread.
- Shadow plane: When you focus the light on the object how it will look. For example if you focus the torch on the sphere from its centre the shadow always looks like a circle. Shadows are a good way to illustrate three dimensional objects that can be viewed in two dimensions. Keep a torchlight right in front of a cone; it will cast shadow in front of the screen.
- Object from certain angles: A third way is by looking at objects from certain angles to get different views. If you see objects from different angles like front view, top view and side view.
Ques: What are the differences between 3D and 2D objects? (2 Marks)
Ans: In three dimensional objects you can see different shapes in the same objects. For example if you see a pyramid from top you can see only a square but when you see it from the side you can see a triangle. Figures only have lengths and breadths are called two dimensional figures.
Ques: What is meant by sectioning? Explain with a diagram. (2 Marks)
Ans: A section will show its true shape when viewed in the normal direction. To find the true shape of a section, it must be a projection of the plane parallel to the section plane. The internal hidden details of the object are shown in orthographic views of dashed lines.
Also Read:
Comments