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

1. Identify the nets which can be used to make cubes (cut out copies of the nets and try it): 

Ans: Cube's nets are \[\left( {ii} \right),{\text{ }}\left( {iii} \right),{\text{ }}\left( {iv} \right){\text{ and }}\left( {vi} \right).\]

2. Dice are cubes with dots on each face. Opposite faces of a die always 

have a total of seven dots on them. 

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Here are two nets to make dice (cubes); the numbers inserted in each square indicate 

the number of dots in that box.

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Insert suitable numbers in the blanks, remembering that the number on the 

opposite faces should total to \[7.\]

Ans:

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3. Can this be a net for a die? Explain your answer.

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Ans: one pair of opposite faces will have \[1{\text{ and }}4\] on them and another pair of opposite faces will have \[3{\text{ and }}6\] on them whose total is not equal to \[7.\]

Therefore, this cannot be a net for a die.

4. Here is an incomplete net for making a cube. Complete it in at least two different 

ways. Remember that a cube has six faces. How many faces are there in the net here? 

(Give two separate diagrams. If you like, you may use a squared sheet for easy 

manipulation.)

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Ans: In the given net there are \[3\] faces.

It can be completed as,

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5. Match the nets with appropriate solids:

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Ans:

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Exercise 15.2

1. Use isometric dot paper and make an isometric sketch for each one of the given 

shapes:

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Ans:

(I)

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(ii)

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(iii)

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(iv)

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2. The dimensions of a cuboid are \[5\] cm, \[3\]cm and \[2\] cm. Draw three different isometric 

sketches of this cuboid.

Ans: The dimensions of given cuboid are $5\;{\text{cm}},\,\,3\;{\text{cm}}$ and $2\;{\text{cm}}$ 

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Three different isometric sketches are,

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3. Three cubes each with $2\;{\text{cm}}$ edge are placed side by side to form a cuboid. Sketch an 

oblique or isometric sketch of this cuboid.

Ans: Oblique sketch is,

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Isometric sketch is,

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4. Make an oblique sketch for each one of the given isometric shapes:

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Ans: Oblique sketches are,

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5. Give (i) an oblique sketch and (ii) an isometric sketch for each of the following:

(a) A cuboid of dimensions $5\;{\text{cm}},\,\,3\;{\text{cm}}$ and $2\;{\text{cm}}$. (Is your sketch unique?)

Ans:

         (i) Oblique sketch                 (ii) Isometric sketch

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(b) A cube with an edge $4\;{\text{cm}}$ long.

Ans: 

             (i) Oblique sketch                               (ii) Isometric sketch

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6. An isometric sheet is attached at the end of the book. You could try to make on it 

some cubes or cuboids of dimensions specified by your friend.

Ans: Cubes and cuboids shapes on isometric sheet is,

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Exercise 15.3

1. What cross-sections do you get when you give a:

(i) vertical cut (ii) horizontal cut to the following solids?

(a) A brick

(b) A round apple

(c) A die

(d) A circular pipe

(e) An ice-cream cone.

Ans:

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Exercise 15.4

1. A bulb is kept burning just right above the following solids. Name the shape of the

 shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You

 may try to experiment first and then answer these questions)

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Ans:

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2. Here are the shadows of some \[{\text{3 - D}}\] objects, when seen under the lamp of the 

overhead projector. Identify the solid (s) that match each shadow. (There may be 

multiple answers for these!)

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Ans:

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3. Examine if the following are true statements: 

(i) The cube can cast a shadow in the shape of a rectangle. 

Ans: The statement is true.

(ii) The cube can cast a shadow in the shape of a hexagon.

Ans: The statement is false.

NCERT Solutions for Class 7 Maths Chapter 15 – Free PDF Download

Class 7 Chapter 15 Includes:

Exercise 15.1 Solutions: 5 Questions (2 Short Questions and 3 Long Questions).

Exercise 15.2 Solutions: 5 Questions (1 Short question and 4 Long questions).

Exercise 15.3 Solutions: 1 question (MCQ).

Exercise 15.4 Solutions: 3 questions (1 short question and 2 long questions).

Introduction

Solid Shapes or figures are very common in our surroundings. We come across these solid shapes in the form of laptops, mobile phones, computers, ice-cream cones, tin cans, and so many other things. These solid shapes have length, breadth, and height.

Facts

• Figures that are drawn on a paper are called plane figures, such as circle, triangle, square, cube, rectangle, etc.

• The solid figures that occupy space are spheres, cones, cylinders, cuboids, cubes, etc.

• The 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 skeleton-outline of a 2-D solid which when folded results in a 3-D shape. A solid can have more than one net.

• Different sections of a solid are viewed either by slicing it or by observing its 2-D shadow. It can also be viewed from the front, top, or side.

The following are examples of 2-Dimensional Shapes.

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Properties of 2 - Dimensional Shapes

1. A two-dimensional solid has two dimensions length and breadth.

2. The shape of a 2-D solid will always depend on two coordinates.

The following are examples of 3-Dimensional Shapes.

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Properties of 3 - Dimensional Shapes

1. A three-dimensional shape has length, breadth, and height. 

2. It has depth. 

3. All things that we see and touch in our environment are three-dimensional solids. 

4. The inside and outside of a 3-D solid are separated by a surface.

5. 3-D solids have faces, vertices, edges, and volume. This property helps you to differentiate between 2-D and 3-D solids.

6. Some examples are pyramids, cones, spheres, cylinders, prisms, etc.

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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.

Example: A cube has 8 vertices, 12 edges, and 6 faces.

Formula: If F, E, and V denote the number of faces, edges, and vertices of a cube respectively, then we have:

F – E + V = 2

Description of Some Basic Shapes

1. Square: It has four sides and four corners. All the sides of a square are of the same length. For example, a sandwich, napkin, chessboard, etc.

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2. Rectangle: A rectangle has four sides and four corners. The opposite sides of a rectangle are of the same length. For example, a table, laptop, mobile phone, etc.

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3. Triangle: A triangle has three sides and three vertices. For example, traffic lights, etc.

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4. Cuboid: A cuboid has six flat surfaces, twelve straight edges, and eight vertices. For example, book, lunch box, cabinet, cubicles, etc.

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5. Cube: A cube has six flat faces, eight vertices, and 12 straight edges. For example, dice, sugar cube, etc.

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6. Cylinder: A cylinder has three faces: 1 curved face and 2 flat faces. It has two curved edges. For example, a gas cylinder, tin-can, pipes, candle, etc.

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7. Cone: A cone has two faces, one slant face, and one flat face. For example, ice-cream cone, funnel, etc.

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Solid Shape

A solid can be sketched in two ways.

1. An oblique sketch is drawn on a squared paper and does not indicate exact measurement but conveys all important aspects of the appearance of the solid.

2. An isometric sketch is drawn on a 3-D drawing paper and has proportional measurements of the solid.

Note: In the case of an isometric sketch the measurements are exact whereas it is not so for an oblique sketch. 

We can view different sections of a solid in many ways:

1. When we slice the shape, it results in the cross-section of the solid.

2. We can observe a 2-D shadow of a 3-D shape.

3. We can look at the shape from different angles, i.e., the front-view, the side-view, and the top-view.

Description of Some More Solid Shapes

1. Triangular Prism: A triangular prism resembles a kaleidoscope. It has triangular bases. There are five faces, nine edges, and six vertices in a triangular prism.

2. Triangular Pyramid: A triangular pyramid is also called a tetrahedron. It has a triangular base. There are four faces, six edges, and four vertices in a triangular pyramid.

3. Square Pyramid: A square pyramid has a square base. It has five faces, eight edges, and five vertices.

4. Sphere: A sphere has no flat face. It has only a spherical face. A sphere has one face, no edges, and no vertices.

Polyhedrons

A solid made up of polygon regions is called a polyhedron. For example, cubes, cuboids, prisms, and pyramids are polyhedrons. Please note that spheres, cylinders, and cones are not polyhedrons because 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 on the surface of a polygon lies inside or on the polygon, the polygon is called a convex polyhedron.

Regular Polyhedrons

Regular polygons whose faces are regular and they meet at each vertex, are called regular polyhedrons.

Prism

A prism is a polyhedron shape whose base and top are congruent and the lateral faces are parallelograms.

Types of Prism

1. Triangular prism

2. Rectangular prism

3. Pentagonal prism

4. Hexagonal prism

5. Pyramid

6. Triangular pyramid

7. Rectangular pyramid

8. Square pyramid

9. Pentagonal pyramid

10. Hexagonal pyramid

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Nets for Building a 3 - D Shape

Geometry net is a skeleton-outline of a 2-D solid which when folded results in a 3-D shape. A net can be used in order to find the surface area of an object.

Net is a 2-D representation of a 3-D object that is unfolded along its edges. A three-dimensional shape may have different nets.

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Why Should You Use Vedantu’s NCERT Solutions for Class 7 Maths?

Key Features of NCERT Solutions: These solutions are designed to help students achieve proficiency in their studies. They are crafted by experienced educators who excel in teaching Class 7 Maths. Some of the features include:

• Comprehensive explanations for each exercise and questions, promoting a deeper understanding of the subject.

• Clear and structured presentation for easy comprehension.

• Accurate answers aligned with the curriculum, boosting students' confidence in their knowledge.

• Visual aids like diagrams and illustrations to simplify complex concepts.

• Additional tips and insights to enhance students' performance.

• Chapter summaries for quick revision.

• Online accessibility and downloadable resources for flexible study and revision.

Conclusion

The NCERT Solutions for Class 7 Maths Chapter 15 - Visualising Solid Shapes, provided by Vedantu, is a valuable tool for Class 7 students. It helps introduce Maths concepts in an accessible manner. The provided solutions and explanations simplify complex ideas, making it easier for Class 7 students to understand the material. By using Vedantu's resources, Students can develop a deeper understanding of NCERT concepts. These solutions are a helpful aid for grade 7 students, empowering them to excel in their studies and develop a genuine appreciation for “Visualising Solid Shapes”.