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NCERT Solutions for Class 7 Maths Chapter 15 – Visualising Solid Shapes

NCERT Solutions for Class 7 Maths Chapter 15 is about Visualizing Solid Shapes. This chapter takes a step forward from the previous Chapter 14 of NCERT for Class 7 Maths Symmetry. In this chapter, there are a total of 4 exercises and 15 questions. The Chapter covers the faces, vertices, and angles. We also study nets for building 3-D shapes, drawing solids on a flat surface and viewing different sections of a solid.

Try these NCERT Solutions for Class 7 Maths Chapter 15 ‘Visualizing Solid Shapes’ which are based on the latest syllabus approved by CBSE. Instasolv provides the most reliable study material for Class 7 Maths. We provide chapter-wise comprehensive solutions of NCERT Class 7 Maths Book that help you in understanding the concepts of each topic in an easy way.

Chapter 15 ‘Visualizing Solid Shapes’ of CBSE NCERT Class 7 Maths Book lays the foundation for more complex mathematics and scientific studies you will take up in the future. For the Maths subject in Class 7, we explain the important elements and summarise each part of the Chapter. To prepare well for the CBSE exams, we suggest you follow our NCERT Solutions.

NCERT Solutions for Class 7 Maths Chapter 15 Visualizing Solid Shapes: Important Topics

Introduction: Plane Figures and Solid Shapes 

  • In this chapter, we will understand the concept of dimension. Every object occupies space and has dimensions. 2-D stands for two dimensional and 3-D stands for three dimensional. 
  • On a plane surface, any figure drawn has two dimensions and one can find out the area of the figure. An object which has three dimensions occupies space or one can measure its volume.

Faces, Edges, and Vertices 

  • In a three dimensional object, for example, a cube, it has six sides which can be drawn or measured in two dimensions. These six sides are called the faces.
  • The points where each face meets another is called a vertex. There are eight such corners or vertices in a cube.
  • The boundary of every face is an edge. These twelve edges or line segments of a cube form its basic skeleton. 

Nets for Building 3-D Shapes 

  • A net is like a skeleton-outline in two dimensions for a three-dimensional object. This net when folded should form the 3-D shape. 

For Example, A cardboard box can be flattened into a two-dimensional figure which is the net for the cardboard box. 

  • Visualization has to be practiced to get a better grasp of the concept. For example an ice cream cone. If you want to build a bet for an ice cream cone, you have to find how you can flatten the cone into a two-dimensional shape. If you cut the cone from the vertex through its length, the cone can be opened up to form a flat or two-dimensional shape. 
  • Now, let us consider a pyramid. It is a square base with four triangles on the sides that meet at a single point at the top. Suppose you have to build a net for the pyramid now, imagine that the triangles separate and fall flat on the ground, symmetrically placed each on one side of the square. This forms the net for the pyramid.

For every 3-D object, the net will have to be visualized. It will be different for different shapes. 

  • Drawing Solids on a Flat Surface

Paper is a flat surface. When a 3-D object like a cube is drawn on paper a visual illusion of the third dimension has to be created. Two techniques are discussed below

Oblique Sketches

  • For a 3-D object let us understand the three dimensions. Most of our graphs made on plain paper have two axes which we generally denote as X-axis and Y-axis. These are drawn perpendicular to each other. Consider a third axis called the Z-axis which is the third dimension and perpendicular to both X-axis and Y-axis. When we draw it on a plain paper we draw it at an angle that is equal in measure from both X-axis and Y-axis. 
  • The angle that Z-axis makes with each X and Y axis is one hundred and thirty-five degrees. While in real terms Z-axis is perpendicular to both the X and Y-axis. By this, you can see that to create a visual illusion an obliqueness has to be used.

Isometric Sketches

An isometric dot sheet divides the paper into small equilateral triangles made up of dots or lines. To draw sketches in which measurements also agree with those of the solid, we can use isometric dot sheets.

Visualizing Solid Objects

Instasolv recommends that you practice this well. You can do the self-practice exercises given in NCERT Class 7 Maths Chapter 15 Visualizing Solid Shapes. 

Viewing Different Sections of a Solid

  • One Way to View an Object is by Cutting or Slicing

Consider an unsliced loaf of bread. It is a solid shape in three dimensions. Every slice of this loaf is a cross-section of the loaf and represents one face of the shape of the loaf. Slicing or cutting can also be done lengthwise and will represent the other face of the shape of the loaf. Across the base, if a slice is cut it represents the third dimension. 

You can also practice this by seeing the cutting of various vegetables that are done in your kitchen.

  • Another Way is by Shadow Play

A shadow is a two-dimensional illustration of a three-dimensional object. Notice your own shadow to understand this better. Also, use a torch to create shadows of different objects to practice. Practice is important for you to understand the concept and visualize solid shapes. 

  • A Third Way is by Looking at it from Certain Angles To Get Different Views

You can physically look at different views of an object like side views, top view, front view. Consider a hut with a slanting thatched roof. The front view is the one where the door to enter the hut is. In the front view, the slant of the roof can be seen. In the side view and top view, you can only see rectangles based on the length of the sides and no slant of the roof can be seen. 

Study Tips for NCERT Class 7 Maths  Chapter 15: Visualizing Solid Shapes

Every student aims to get a high score in the exams. Instasolv recommends that you read chapter 15 Visualizing Solid Shapes of CBSE NCERT Solutions for Class 7 Maths. Instasolv has provided a simple explanation and summary of each part. All of this can be used to develop a better understanding of all the concepts. 

  • If any concept is still not understood, ask the experts on the Instasolv app.
  • This chapter requires good visualization. Many of the answers will be found directly in the summary. To help you solve other questions, here are a few more tips:
    1. Notice the cross-sections of various vegetables when they are chopped in your kitchen.
    2. Use a torch or a light to create shadows of different objects
    3. View objects from different angles and draws them. The common views to be drawn are top view, side view and front view. For example, consider a cricket bat. In the front view, you can see the outline of the front of the bat and the handle in rectangular shapes. In the side view, you can see a thin rectangle of the bat behind which is a triangle representing the protrusion at the back of the bat. the handle in this view is similar to that as in front view. In the top view, the handle will look like a circle and the bat face will be a combination of the side views from either side.
  • There are several self-practice exercises that we recommend that you do all of them without looking at the NCERT Solutions. 
  • Play the games illustrated in the Chapter with your friend.
  • Notice the cross-sections of various vegetables when they are chopped in your kitchen.
  • Use a torch or a light to create shadows of different objects

Learning by rote is never recommended by the subject matter experts of Instasolv. Only practice will help you develop an understanding of the concepts and Visualizing Solid Shapes. 

Follow these class 7 maths chapter 15 NCERT Solutions and tips provided and, score high marks in your Maths examination.