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Visualising Solid Shapes Class 7 Notes Maths

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.

Visualising Solid Shapes Class 7 Notes Maths

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.

Visualising Solid Shapes Class 7 Notes Maths

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.

Visualising Solid Shapes Class 7 Notes Maths

  • 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?
View Solution

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

Visualising Solid Shapes Class 7 Notes Maths

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.

Visualising Solid Shapes Class 7 Notes Maths

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

Visualising Solid Shapes Class 7 Notes Maths


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

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

Visualising Solid Shapes Class 7 Notes Maths

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 ShapesNets 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?
View Solution

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.

Visualising Solid Shapes Class 7 Notes Maths


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.

Visualising Solid Shapes Class 7 Notes Maths

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.

Visualising Solid Shapes Class 7 Notes Maths

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

The document Visualising Solid Shapes Class 7 Notes Maths is a part of the Class 7 Course 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.
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