NCERT Solutions for Class 7 Mathematics Chapter 15 Visualising Solid Shapes
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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
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, frontview, sideviews, and the topview.
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
Chapter 15 – Visualizing Solid Shapes Exercises  
Exercise 15.1  Questions & Solutions 
Exercise 15.2  Questions & Solutions 
Exercise 15.3  Questions & Solutions 
Exercise 15.4  Questions & Solutions 
Introduction
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, icecream cones, and many other things. These solid shapes have 3 dimensions ;length, breadth, and height.
Facts
 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 2dimensional, and solid shapes are 3dimensional.
 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.
 3D solids can be represented in 2D by drawing their oblique sketches or isometric sketches.
 A net is a 2D skeleton outline that results in a 3D 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 2D shadow. It can also be viewed from the front, top, or side.
Properties of 2 – Dimensional Shapes
 A 2dimensional solid has two dimensions, length and breadth.
 The shape of a 2D solid will always depend on two coordinates.
Properties of 3 – Dimensional Shapes
 A 3D shape has length, breadth, and height.
 All things that we see and touch in our surroundings are 3D solids.
 A surface separates the inner and outside of a 3D solid.
 3D solids have faces, vertices, edges, and volume. This property helps you to differentiate between 2D and 3D solids.
 Some examples of 3D 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, icecream cones, funnels, etc.
Solid Shape
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 3D 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.
Polyhedrons
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.
Convex 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 Polyhedrons
Regular polygons having identical regular faces which meet at each vertex.
Prism
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
 Pyramid
 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 2D solid, which results in a 3D shape when folded. A net can be utilised to find the surface area of an object.
Net is a 2D representation of a 3D object unfolded along its edges. A 3dimensional 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 chapterwise solutions for each subject.
$\begin{array}{l}\text{Q.1 Identify the nets which can be used to make cubes}\\ \text{(cut out copies of the nets and try it):}\end{array}$
Ans
$\left(i\right)\mathrm{The}\mathrm{given}\mathrm{net}\mathrm{can}\mathrm{be}\mathrm{folded}\mathrm{as}:$
\begin{array}{l}\text{When the faces that are in sky blue colur and in pink colour}\\ \text{are folded to make cube, they will be overlaping each other}\text{.}\end{array} \text{} \text{(ii) The given net can be folded as:} \text{}
\text{Thus, a cube can thus be formed in above way}\text{.} \text{} \text{(iii) The given net can be folded as:} \text{}
\text{Thus, a cube can thus be formed in above way}\text{.} \text{} \text{(iv) The given net can be folded as:} \text{}
\text{Thus, a cube can thus be formed in above way}\text{.} \text{} \text{(v) The given net can be folded as:} \begin{array}{l}\text{}\end{array}
\begin{array}{l}\text{When the faces are in blue colour and in red colour are folded}\\ \text{to make a cube, they will be overlapping each other}\text{.}\end{array} \begin{array}{l}\text{(vi) The given net can be folded as:}\end{array} \text{}
\text{Thus, a cube can thus be formed in above way}\text{.}
$\begin{array}{l}\text{Q.2}\end{array}$ $\begin{array}{l}\text{Dice are cubes with dots on each face. Opposite faces of}\\ \text{a die always have a total of seven dots on them.}\end{array}$
$\begin{array}{l}\text{Here are two nets to make dice}\left(\text{cubes}\right)\text{; the numbers}\\ \text{inserted in each square indicate the number of dots in}\\ \text{that box.}\end{array}$
$\begin{array}{l}\text{Insert suitable numbers in the blanks, remembering that}\\ \text{the number on the opposite faces should total to 7.}\end{array}$
Ans
\begin{array}{l}\text{(i) The numbers can be inserted as follows so as to make the}\\ \text{given net into a net of a dice}\text{.}\end{array}
\begin{array}{l}\text{It can be seen that the sum of opposite faces is 7}\text{.}\\ \\ \text{(ii) The numbers can be inserted as follows so as to make the}\\ \text{given net into a net of a dice}\text{.}\end{array} \text{}
\text{It can be seen that the sum of opposite faces is 7}\text{.}
$\begin{array}{l}\text{Q.3}\end{array}$ $\text{Can this be a net for a die? Explain your answer.}$
Ans
\text{The given net can be folded as:}
\begin{array}{l}\text{It can be observed that the opposite face of the dice so formed}\\ \text{have 2 and 5, 1 and 4, 3 and 6 on them}\text{.}\\ \text{The sum of numbers on the opposite faces comes to 7, 5 and 9}\\ \text{respectively}\text{.}\\ \text{However, in case of a dice, the sum of numbers on the opposite}\\ \text{faces should be7}\text{.}\\ \text{Therefore, this net is not of a dice}\text{.}\end{array}
$\begin{array}{l}\text{Q.4}\end{array}$
$\begin{array}{l}\text{Here is an incomplete net for making a cube. Complete}\\ \text{it in at least two different ways. Remember that a cube}\\ \text{has six faces. How many are there in the net here?}\\ \text{(Give two separate diagrams. If you like, you may use a}\\ \text{squared sheet for easy manipulation.)}\end{array}$
Ans
\text{There are 3 faces given in the net}\text{. The given net can be completed as:}
$\begin{array}{l}\text{Q.5}\end{array}$
Match
Ans
\text{Consider net (i) It can be folded as:}
\text{Consider net (ii) It can be folded as:}
\text{It is a net of cube}\text{. Hence, (a) is the correct option}\text{.} \text{} \text{Consider net (iii) It can be folded as:} \text{}
\text{It is a net of cylinder}\text{. Hence, (b) is the correct option}\text{.} \text{} \text{Consider net (iv) It can be folded as:}
\text{It is a net of cone}\text{. Hence, (c) is the correct option}\text{.}
$\begin{array}{l}\text{Q.6}\end{array}$
$\mathrm{Use}\mathrm{isometric}\mathrm{dot}\mathrm{paper}\mathrm{and}\mathrm{make}\mathrm{an}\mathrm{isometric}\mathrm{sketch}\mathrm{for}\mathrm{each}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{shapes}:$
Ans
$\begin{array}{l}\text{Q.7}\end{array}$
The dimensions of a cuboid are 5 cm, 3 cm and 2 cm.
Ans
$\begin{array}{l}\text{Q.8}\end{array}$
Three cubes each with 2 cm edge are placed side by side
Ans
$\begin{array}{l}\text{Q.9}\end{array}$
Make an oblique sketch for each one of the given isometric shapes:
Ans
$\begin{array}{l}\text{Q.10}\end{array}$
Give
Ans
\text{(i) oblique sketch:}
\text{(ii) Isometric sketch:}
$\begin{array}{l}\text{Q.11}\end{array}$
What crosssections do you get when you give a
Ans
$\begin{array}{l}\text{(a) A brick}\\ \text{We can give a vertical cut to a brick in the following way:}\end{array}$
\begin{array}{l}\text{(b) A round apple}\\ \text{We can give a vertical cut to a roudn apple in the following way:}\end{array}
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:
\text{We can give a horizontal cut to a die in the following way:} \begin{array}{l}\text{}\end{array}
\begin{array}{l}\text{(d) A circular pipe}\\ \text{We can give a vertical cut to a circular pipe in the following way:}\end{array}
\text{We can give a horizontal cut to a circular pipe in the following way:} \begin{array}{l}\text{}\end{array}
\begin{array}{l}\text{(e) An ice cream cone}\\ \text{We can give a vertical cut to an ice cream cone in the following way:}\end{array}
$\mathrm{We}\mathrm{can}\mathrm{give}\mathrm{a}\mathrm{horizontal}\mathrm{cut}\mathrm{to}\mathrm{an}\mathrm{ice}\mathrm{cream}\mathrm{cone}\mathrm{in}\mathrm{the}\mathrm{following}\mathrm{way}:$
$\begin{array}{l}\text{Q.12}\end{array}$
A bulb is kept burning just right above the following solids.
Ans
\begin{array}{l}\text{The shapes of the shadows of these figures will be as follows:}\\ \text{(i) A ball}\end{array}
\text{The shape of the shadow of a ball will be a circle}\text{.} \text{(ii) A cylindrical pipe}
\text{The shape of the shadow of a cylindrical pipe will be a rectangle} \text{}\text{.} \text{} \text{(iii) A book}
\text{} \text{The shape of the shadow of a book will be a rectangle}\text{.}
$\begin{array}{l}\text{Q.13}\end{array}$
$\begin{array}{l}\text{Here are the shadows of some 3D objects, when seen}\\ \text{under the lamp of an over head projector. Identify the}\\ \text{solid}\left(\text{s}\right)\text{that match each shadow. (There may be}\\ \text{multipleanswers for these!).}\end{array}$
Ans
\begin{array}{l}\text{The given shadows can be obtained in case of the following}\\ \text{objects}\text{.}\\ \text{(i) Compact disk (Sphere)}\\ \text{(ii) A}\text{}\text{dice (Cube)}\\ \text{(iii) Triangular pyramid (Cone)}\\ \text{(iv) Note Book (Cuboid)}\end{array}
$\begin{array}{l}\text{Q.14}\end{array}$
$\begin{array}{l}\text{Examine if the following are true statements:}\\ \left(\text{i}\right)\text{The cube can cast a shadow in the shape of a rectangle.}\\ \left(\text{ii}\right)\text{The cube can cast a shadow in the shape of a hexagon.}\end{array}$
Ans
\begin{array}{l}\text{A cube can cast shadow only in the shape of a square}\text{.}\\ \text{Therefore, any other shapes are not possible}\text{.}\\ \text{So,}\\ \text{(i) False}\\ \text{(ii) False}\end{array}
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FAQs (Frequently Asked Questions)
1. How can the chapter Visualising Solid Shapes help students in daily life?
Visualising solid shapes aims to make students comprehend 3D 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.
2. How can the NCERT Solutions for Class 7 Mathematics Chapter 15 help students?
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.
3. How to access NCERT solutions class 7 Mathematics chapter 15?
NCERT Solutions for Class 7 are available on Extramarks’ official website.