Class 7 is one of those classes which has great importance in forming a strong base for higher studies of any subject. There are many topics that students of Class 7 learn in Mathematics for the first time.
To help Class 7 students with their Mathematics preparation, Extramarks offers NCERT Solutions for Class 7 Mathematics Chapter 15 where students will find detailed solutions to the questions given in this chapter of their NCERT textbook. Many students find it difficult to solve all the questions in the textbook on their own. These resources will help guide them in the right direction so that they can feel confident when they appear for their final exams.
NCERT Solutions for Class 7 Mathematics Chapter 15
Access NCERT Solutions for Class 7 Mathematics Chapter 15 – Visualising Solid Shapes
NCERT Solutions for Class 7 Mathematics Chapter 15
Chapter 15 of Class 7 NCERT Mathematics textbook introduces students to the different ways of visualising 3D shapes. The chapter includes a lot of interactive exercises that students can try on their own to get a perspective on the topic.. The chapter starts by explaining the differences between 2D and 3D shapes and the relationships between the two. It talks about ‘nets’ which are skeleton- outlines in 2D that can be folded into 3D solid shapes.
In this chapter, students will also learn about the different ways of visualising solid shapes including the shadow view, front-view, side-views, and the top-view.
Class 7 Chapter 15 Includes
The topics included in Chapter 15 are the following:
- Introduction: Plane figures and Solid shapes
- Faces, Edges, and Vertices
- Nets for Building 3D shapes
- Drawing Solids on a Flat Surface
- Visualising Solid Objects
- Viewing Different Sections of a Solid
The chapter also includes the following exercises. Students can find the solutions to these exercises in NCERT Solutions for Class 7 Mathematics Chapter 15 by Extramarks
Exercise 15.1: 5 Questions (2 Short and 3 Long Questions).
Exercise 15.2: 5 Questions (1 Short and 4 Long questions).
Exercise 15.3: 1 question (MCQ).
Exercise 15.4: 3 questions (1 short and 2 long questions).
Solid Shapes or figures are very prominent in our surroundings. We come across these solid shapes in the form of mobile phones, laptops, computers, tin cans, ice-cream cones, and many other things. These solid shapes have 3 dimensions ;length, breadth, and height.
- Figures drawn on paper are called plane figures, such as circles, triangles, squares, cubes, rectangles, etc.
- The figures that acquire space are called solid shapes, such as spheres, cones, cylinders, cuboids, etc.
- Plane figures are 2-dimensional, and solid shapes are 3-dimensional.
- The corners of a solid are called its vertices, the line segments joining its vertices are called its edges, and its surfaces are called faces.
- 3-D solids can be represented in 2-D by drawing their oblique sketches or isometric sketches.
- A net is a 2-D skeleton outline that results in a 3-D shape when folded. A solid can have more than one net.
- Different sections of a solid are viewed either by slicing it or examining its 2-D shadow. It can also be viewed from the front, top, or side.
Properties of 2 – Dimensional Shapes
- A 2-dimensional solid has two dimensions, length and breadth.
- The shape of a 2-D solid will always depend on two coordinates.
Properties of 3 – Dimensional Shapes
- A 3-D shape has length, breadth, and height.
- All things that we see and touch in our surroundings are 3-D solids.
- A surface separates the inner and outside of a 3-D solid.
- 3D solids have faces, vertices, edges, and volume. This property helps you to differentiate between 2-D and 3-D solids.
- Some examples of 3-D shapes are pyramids, cones, spheres, cylinders, prisms, etc.
Faces, Edges, and Vertices
Face: The flat surface of a solid is called a face.
Edge: A line that joins two corners of a solid is an edge.
Vertices: The corners of a solid are its vertices.
Description of Some Basic Shapes
- Square: It has four sides and four corners, and all the sides of a square are of the same length. For example, a napkin, a sandwich, a chessboard, etc.
- Rectangle: A rectangle has four sides and four corners. The opposite sides of a rectangle are of the same length. For example, a tablet, mobile phone, laptop, etc.
- Triangle: A triangle has three sides and three vertices. For example, traffic lights.
- Cuboid: A cuboid has six flat surfaces, twelve straight edges, and eight vertices. For example, books, cabinets, lunch boxes, etc.
- Cube: A cube has six flat faces, eight vertices, and 12 straight edges. For example, sugar cubes, dice, etc.
- Cylinder: A cylinder has three faces, 1 curved face and 2 flat faces. It has two curved edges. For example, a gas cylinder, pipes, candle, etc.
- Cone: A cone has two faces, one slant face and one flat face. For instance, ice-cream cones, funnels, etc.
A solid can be sketched in two ways.
- An oblique sketch is drawn on squared paper and does not reflect exact measurement but expresses all important aspects of the formation of the solid.
- An isometric sketch is drawn on a 3-D drawing paper and has proportional measurements of the solid.
Description of Some More Solid Shapes
- Triangular Prism: It resembles a kaleidoscope. It has a triangular base with 5 faces, 9 edges, and 6 vertices.
- Triangular Pyramid: It is also named as a tetrahedron. It has a triangular base with 4 faces, 6 edges, and 4 vertices.
- Square Pyramid: It has a square base with 5 faces, 8 edges, and 5 vertices.
- Sphere: It has no flat face. It has only a spherical face. A sphere has 1 face, no edges, and no vertices.
A solid composed of polygon regions is named a polyhedron. For instance, cubes, prisms, cuboids, and pyramids are polyhedrons. Spheres, cylinders, and cones are not polyhedrons as they are not made up of polygon regions. There are two types of polyhedrons- Convex polyhedrons and Regular polyhedrons.
When a line segment joining any two points within the surface of a polyhedron lies completely inside or on the shape, the polyhedron is called a convex polyhedron.
Regular polygons having identical regular faces which meet at each vertex.
It is a polyhedron shape whose base and top are congruent, and the lateral faces are parallelograms.
Types of Prism
- Triangular prism
- Rectangular prism
- Pentagonal prism
- Hexagonal prism
- Triangular pyramid
- Rectangular pyramid
- Square pyramid
- Pentagonal pyramid
- Hexagonal pyramid
Nets for Building a 3 – D Shape
Geometry net is a skeleton outline of a 2-D solid, which results in a 3-D shape when folded. A net can be utilised to find the surface area of an object.
Net is a 2-D representation of a 3-D object unfolded along its edges. A 3-dimensional shape may have many different nets.
NCERT Solutions for Class 7 Mathematics
CBSE Class 7 Mathematics consists of 15 chapters. All these chapters are very essential for the students at this level. In addition to the NCERT Solutions for Class 7 Mathematics Chapter 15, you can access solutions for all the other 15 chapters from the Extramarks website and refer to them for daily practise. Here are some of the benefits of referring to NCERT Solutions for Class 7.
- The solutions are prepared by subject experts who have years of experience in teaching.
- All the answers are stated stepwise for quick retention.
- Every answer of every chapter in NCERT Solutions for Class 10 Science is written as per the CBSE guidelines.
- As the explanations are comprehensive, the fundamentals of the chapter are understood by the students in a better way.
- The answers in NCERT solutions are explained in detail, which gives students an idea of how to attempt a question in the board exam in the right manner.
NCERT Solutions for Class 7
Along with Mathematics, Extramarks provides NCERT solutions for all the subjects. Students can access the chapter-wise solutions for each subject.
The dimensions of a cuboid are 5 cm, 3 cm and 2 cm.
Three cubes each with 2 cm edge are placed side by side
Make an oblique sketch for each one of the given isometric shapes:
What cross-sections do you get when you give a
We can give a horizontal cut to a round apple in the following way:
(c) A die
We can give a vertical cut to a die in the following ways:
A bulb is kept burning just right above the following solids.
FAQs (Frequently Asked Questions)
Visualising solid shapes aims to make students comprehend 3-D space and how objects are formed in such space. They are trained to create frames of desired shapes and then construct those shapes by using prepared edges or cuttings.
NCERT Solutions for Class 7 Mathematics Chapter 15 are an effective guide in understanding the whole chapter completely. These solutions include answers to every problem in every exercise of chapter 15. Students can get conceptual knowledge with these solutions and get good scores in the exams.
NCERT Solutions for Class 7 are available on Extramarks’ official website.