NCERT Solutions for Class 7 Maths Chapter 13 – Visualising Solid Shapes

Visualising Solid Shapes Summary

Geometry is not just about lines on paper; it is about the world around us. In Chapter 13, students learn about three-dimensional shapes instead than just two-dimensional ones. A solid shape is an object that takes up space and has three dimensions: length, width, and height.

Some of the main ideas in this Class 7 Chapter 13 maths NCERT solutions are:

• Dimensions: Knowing the difference between 2D (two-dimensional) and 3D (three-dimensional) shapes.

• Elements of Solids: Finding vertices (corners), edges (lines where faces connect), and faces (flat surfaces).

• Nets for 3D Shapes: Learning how to fold a 2D skeleton into a 3D shape.

• Representing Solids: Using oblique and isometric sketches to make 3D shapes on 2D paper.

• Seeing Things: Learning how the same thing looks different from the front, side, and top.

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Types of Solid Shapes

You need to know the most common solid shapes before you can answer questions:

• Cube: All of its sides are square, like a die.

• Cuboid: It has rectangular faces, like a book or a box.

• Cylinder: A shape having a round base and a surface that curves, like a pipe.

• Cone: It has a spherical base that gets smaller at the top, like an ice cream cone.

• Sphere: It is perfectly round, like a ball.

These examples help students connect the ideas of visualising solid shapes to what they see in real life.

Faces, Edges, and Vertices

Before you start answering the questions in the visualising solid shapes class 7 question answer sets, you should learn the basic terms.

1. Faces: They are the flat sides of a solid. A cube, for instance, has six square sides.

2. Edges: These are the lines that connect two faces. There are twelve edges on a cube.

3. Vertices: These are the places where three or more edges come together. There are eight points on a cube.

Euler’s Formula in Solid Shapes

Euler's Formula gives us a convenient way to relate faces, edges, and vertices:

F – E + V = 2, where

• F = The number of faces

• E = Number of edges

• V = The number of corners

For instance, in a cube:

6 – 12 + 8 = 2

This method lets you check the shapes of various solid shapes in the NCERT Class 7 visualising solid shapes solutions.

Read More - NCERT Solutions for Class 7 Maths Chapter 1 Integers

NCERT Solutions for Class 7 Maths Chapter 13

Below are selected exercises and conceptual questions from the Class 7 Chapter 13 maths question answer series. These focus on logic and calculation to help you practise without needing complex drawing tools.

Exercise 13.1: Nets and Building Solids

Question 1: Identify the nets which can be used to make cubes.

A net is a 2D pattern that can be folded to make a 3D solid. To form a cube, a net must have exactly six square faces arranged in a way that they do not overlap when folded.

• Logic: A net for a cube cannot have more than four squares in a single row or column without creating an open end or overlap.

• Tip: Look for the "T" shape or "cross" shape patterns, as these are the most common valid nets for cubes.

Question 2: Dice are cubes with numbers on opposite sides that must total up to 7. What numbers should be on the other sides of a net that shows 4, 5, and 6?

• Solution:  * Opposite to 4 must be 3 (since 4 + 3 = 7).

• Opposite to 5 must be 2 (since 5 + 2 = 7).

• Opposite to 6 must be 1 (since 6 + 1 = 7).

Exercise 13.2: Drawing Solids on Paper

This section of the class 7 maths question answer focuses on how we represent depth.

• Oblique Sketches: These do not have proportional lengths but give a good visual idea of the solid.

• Isometric Sketches: These are drawn on dotted paper where measurements are kept proportional.

Question: If you draw a cube of side 3 cm on isometric paper, how many dots will the edges span?

• Answer: The edges will span 3 units of the dotted grid, ensuring that the parallel lines stay equal in length, maintaining the 3D perspective accurately.

Exercise 13.3: Visualising Sections of Solids

Question 1: What cross-section do you get when you give a horizontal cut to a circular pipe?

• Solution: A circular pipe is a cylinder. If you cut it horizontally (parallel to the base), the cross-section will be a circle.

Question 2: What cross-section do you get when you give a vertical cut to a brick?

• Solution: A brick is a cuboid. If you cut it vertically, the resulting face or cross-section will be a rectangle.

Read More - NCERT Solutions for Class 7 Science Chapter 1 Nutrition in Plants

Exercise 13.4: Shadows of Solid Shapes

This activity is about how solids cast shadows when light hits them.

Question 1: What kind of shadow will a cylinder make?

• Solution: From the top → Circle

From the side → Rectangle

Question 2: What kind of shadow does a cone make?

• Solution: Circle from the top

From the side, it's a rectangle.

These questions help improve spatial thinking in visualising solid shapes class 7 NCERT solutions.

Benefits of Using Visualising Solid Shapes Class 7 Question Answer

Structured NCERT solutions benefit students in several ways:

• Better spatial awareness: It's useful in real life to be able to see things from many angles, like whether you're doing art, designing something, or creating something.

• Getting Ready for Tests: These solutions are based on the approved curriculum, so you'll learn everything you need to know to do well on your school tests.

• Nets and cross-sections help the brain understand things and see them in three dimensions.

• Easy to grasp Language: Our visualising solid shapes class 7 question and answer guide doesn't contain any technical words, so it's easy for all youngsters to grasp.

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