Chapter Notes: Visualizing Solid Shapes

# Visualising Solid Shapes Class 7 Notes Maths

 Table of contents Plane Figures and Solid Shapes Faces, Edges and Vertices of 3D Shapes Nets for Building 3D Shapes Drawing Solids on a Flat Surface Viewing Different Sections of a Solid

Look at the picture of the pencil box given below. You can only see its length and width. This picture would be a 2D image because it has only two dimensions: length and width. It's like looking at a flat drawing of your pencil box on a piece of paper.

Now, if you could see your pencil box from all sides, including the top, bottom, front, back, and sides, you would have a 3D image. A 3D image shows all three dimensions: length, width, and height. It's like holding your pencil box in your hands and being able to see it from every angle.

In simple terms, a 2D image is like a flat drawing, and a 3D image is like seeing the real object in front of you.

## Plane Figures and Solid Shapes

Visualizing solid shapes is an essential concept in mathematics, particularly in geometry. Solid shapes, also known as three-dimensional (3D) shapes, exist in physical space and have three dimensions: length, width, and height. Unlike two-dimensional shapes, such as squares and circles, which exist on a flat plane, solid shapes have volume and occupy space.

• Plane figures are flat or 2 -Dimension figures, they have no thickness.
For example: Squares, rectangles, circles, triangles etc.
• Solid Shapes are 3-Dimensional shapes, and they occupy space and have volume.
For example: Cube, cuboid, sphere, cone, hemisphere etc.

Question for Chapter Notes: Visualizing Solid Shapes
Try yourself:
Which of the following shapes is a solid shape?

## Faces, Edges and Vertices of 3D Shapes

### 1. Faces

• A 3D shapes is not flat therefore it has 3 dimensions and these are faces, edges, and vertices.
• Faces are simply the face of a 3D shape or the flat surface of the 3D shape.
For example: The number of faces of cube is 6

### 2. Edges

• Edges are the line segments which join one vertex to another vertex.
For example – Edges in a cylinder are 2 and are shown below.

### 3. Vertices

• Points where two or more edges meet between faces is known vertices of any 3D shape or the corners of 3D shape.
For example: The cube has 8 vertices and is shown below

Question for Chapter Notes: Visualizing Solid Shapes
Try yourself:The number of vertices of a cube is

The table shows the number of the faces, edges and vertices of some shapes.

## Nets for Building 3D Shapes

The net of a three-dimensional solid is a two-dimensional skeleton outline, which, when folded, results in the three-dimensional shape. Net is used for making 3D shapes.

• It is a basic skeleton outline in 2 -Dimensions i.e., it is flat 3-Dimensional shape which can be folded and joined together with the help of glue.
• Nets for building some shapes are shown below

Nets of 3-D Shapes

Question for Chapter Notes: Visualizing Solid Shapes
Try yourself:What cross-section do you get when you give a horizontal cut to a brick?

## Drawing Solids on a Flat Surface

There are two techniques to create the illusion, of three-dimensionality when drawing solid shapes on a flat surface, such as paper.

### 1. Oblique Sketches

• These drawings show how 3D objects look from different angles.
• They're drawn by hand, without using any tools.
• They don't involve measuring the actual size of the 3D object.
• Below is a sketch of a cube drawn from an angle.

### 2. Isometric Sketches

• This method involves both drawing the 3D object and taking measurements.
• The drawings are done on special sheets called isometric sheets.
• Below is a sketch of a cube drawn using the isometric method, with the dotted sheet it's drawn on being called an isometric sheet.

## Viewing Different Sections of a Solid

There are many methods to view different sections of a solid:

(a) Slicing and Cutting: This method reveals the inside of a solid by slicing it into cross-sections.

(b) Shadow Casting: This technique creates a two-dimensional representation of a three-dimensional object by casting its shadow.

(c) Viewing from Different Angles: Observing a solid from various perspectives, such as front, side, and top views, offers valuable insights into its shape and structure.

Example: Different viewpoints of a building are illustrated below.

Question for Chapter Notes: Visualizing Solid Shapes
Try yourself:The shadow of the lamp of an a cube when seen under overhead projector is

The document Visualising Solid Shapes Class 7 Notes Maths is a part of the Class 7 Course Mathematics (Maths) Class 7.
All you need of Class 7 at this link: Class 7

## Mathematics (Maths) Class 7

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## FAQs on Visualising Solid Shapes Class 7 Notes Maths

 1. What are the main components of a 3D shape?
Ans. A 3D shape consists of faces, edges, and vertices.
 2. What is a net in relation to building 3D shapes?
Ans. A net is a 2D representation of a 3D shape that can be cut out and folded to form the actual 3D shape.
 3. How can one draw solids on a flat surface?
Ans. Solids can be drawn on a flat surface by creating their 2D projections or by using isometric drawings.
 4. How can one view different sections of a solid shape?
Ans. Different sections of a solid shape can be viewed by cutting the shape along various planes and examining the resulting cross-sections.
 5. What is the importance of visualizing solid shapes in mathematics?
Ans. Visualizing solid shapes helps in understanding their properties, relationships, and applications in real-world scenarios, making it easier to solve problems related to geometry and spatial reasoning.

## Mathematics (Maths) Class 7

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