NCERT CLASS VII MATHEMATICS

MATHS NOTES TERM-2, PART-11 FEBRUARY 2021

CHAPTER 15: VISUALISING SOLID SHAPES (Activity based chapter)

Plane Figures (2-Dimensional Shape) The figures which we can draw on a flat surface are called Plane Figures. They have two

dimensions i.e. length and breadth, hence these are called 2 Dimensional Shapes.

Solid Shapes (3-Dimensional shapes)

• Solid shapes have length, breadth or width and depth or height.

• They are called 3D or three-dimensional shapes.

• Example: Cuboids, Cylinders, Spheres and Pyramids.

Faces ,Edges and Vertices of a 3-D shape

• Faces – All the flat surfaces of the 3-D figure are the faces of that shape. The faces of 3D

shapes are made by the 2-D shapes.

• Edges – The line segment where the faces of the 3D shape meet with each other are the

edges of that shape.

• Vertices – The corners or the points where the edges meet with each other are the vertices of

the 3D shape. The singular form of vertices is the vertex.

Perspectives of a Solid Shape

Visualizing solid shapes:

• Solid shapes can be visualized in different ways.

• Solid shapes can be formed by placing some solid shapes side by side to form a new solid

shape.

• Example: (i) A cylinder is formed by stacking up circles vertically.

(ii) Cubes can be formed by placing cubes side by side

• A solid can be visualized by breaking it down to the smallest unit.

• For example, a cube of dimensions (3cm x 3cm x 3cm) can be made up of 27 small cubes of

dimensions (1cm x 1cm x 1cm).

Viewing sections of a solid by slicing or cutting:

• If you cut or slice a solid we get to view the cross-section.

Example: If a loaf of bread is cut vertically, then the cross-section is almost a square. But if

it is cut or sliced horizontally, the cross-section is a rectangle.

• Similarly, other solid shapes can be sliced in order to find their 2D cross-sectional

shapes.

Example: A cucumber cut vertically gives a circle.

Viewing sections of a solid by using shadows:

• Shadows can be used to view 3D objects as 2D shapes.

• Example: The shadows of a cylinder are shown below.

Different views of a Solid:

• A solid can be visualized by looking at it from different angles, namely: (i) Front view

(ii) Top view (iii) Side view.

• Example: The different views of a figure are shown below.

Quantities Associated with a Solid

The table below shows the number of faces, edges and vertices some solid shapes have:

Nets of Solid Shapes

Building 3-D objects:

A net is a flattened out skeletal outline or a blueprint of a solid which can be folded along the

edges to create solid.The same solid can have multiple nets.

Example: A net for a cube box.

Representing 3D Shapes on a Paper

Drawing solids on a flat surface:

• Solid shapes can be represented on a 2D flat surface like paper.

• This is done by drawing oblique sketches, to make it appear 3D. This is called as 2D

representation of a 3D solid.

Oblique sketches:

• Oblique sketches do not have the exact length of a solid shape but appears exactly like

the solid shape.

• Example: Drawing an oblique sketch of a cube:

Step 1: Draw the front and the opposite faces.

Step 2: Join the corresponding corners. (Figure 1)

Step 3: Redraw using dotted lines for hidden edges. (Figure 2)

Isometric sketches:

• Isometric sketches have measurements equal to that of the solid.

• They are usually drawn on an isometric dotted paper.

Example: Drawing an isometric sketch of a cuboid of dimensions 4 × 3 × 3:

Step 1: Draw a rectangle to show the front face of the cuboid.

Step 2: Draw four parallel line segments of length three starting from the four corners of the

rectangle.

Step 3: Connect the corresponding corners using appropriate line segments.

Step 4: The figure thus obtained is the isometric sketch of the cuboid.

Exercise 15.1

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

i. No, the net cannot be folded as a cube.

ii. Yes, the given net can be folded as a cube.

iii. Yes, the given net can be folded as a cube.

iv. Yes, the given net can be folded as a cube.

v. No, the given cannot be folded as a cube.

vi. Yes, the given can be folded as a cube.

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

Sol: The given net is folded as dice is shown in figure below,

No, this cannot be a net for a die.

By observing the figure we can say that, one pair of opposite face will have 1 and 4, another

pair of opposite face will have 3 and 6 the sum of these two opposite faces are not equal to 7.

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 are there in the net here? (Give two separate

diagrams. If you like, you may use a squared sheet for easy manipulation.)

Sol: In the given net there are 3 faces and it can be completed as shown below,

5. Match the nets with appropriate solids: (For question refer textbook page 282)

(a) (ii)

(b) (iii)

(c) (iv)

(d) (i)

Exercise 15.2

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

i. sol:

ii. sol:

iii. sol:

iv. sol:

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

of this cuboid.

Solution:-

From the question it is given that dimension of a cuboid are 5 cm, 3 cm, and 2 cm.

The three different isometric sketches of this cuboid is shown below,

1.

2.

3.

3. Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique

or isometric sketch of this cuboid.

Sol: Oblique sketch:

Isometric sketch:

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

(i) sol:

(ii) sol:

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

(a) A cuboid of dimensions 5 cm, 3 cm and 2 cm. (Is your sketch unique?)

(b) A cube with an edge 4 cm long.

Sol: (a) (i) Oblique sketch

(ii) Isometric sketch

(b) (i) Oblique sketch

(ii) Isometric sketch

Exercise 15.3

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

(i) vertical cut (ii) horizontal cut

to the following solids?

Sol: (a) A brick:

The cross-section of a brick when it is cut into vertically is as shown in the figure below,

The cross-section of a brick when it is cut into horizontally is as shown in the figure below,

(b) A round apple:

The cross-section of a round apple when it is cut into vertically is as shown in the figure below,

The cross-section of a round apple when it is cut into horizontally is as shown in the figure

below,

(c) A die:

The cross-section of a die when it is cut into vertically is as shown in the figure below,

The cross-section of a die when it is cut into horizontally is as shown in the figure below,

(d) A circular pipe:

The cross-section of a circular pipe when it is cut into vertically is as shown in the figure below,

The cross-section of a circular pipe when it is cut into horizontally is as shown in the figure

below,

(e) An ice cream cone:

The cross-section of an ice cream when it is cut into vertically is as shown in the figure below,

The cross-section of an ice cream when it is cut into horizontally is as shown in the figure

below,

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).

(i) sol: The shape of the shadow obtained from a ball is circle.

(ii) sol: The shape of the shadow obtained from a cylindrical pipe is rectangle.

(iii) sol: The shape of the shadow obtained from a book is rectangle.

2. Here are the shadows of some 3-D objects, when seen under the lamp of an overhead

projector. Identify the solid(s) that match each shadow. (There may be multiple answers for

these!)

Sol: (i) A circle: Cricket ball, water bottle cap, Disc

(ii) A square: Die, chalk box

(iii) A triangle: Birthday cap etc.

(iv) A rectangle: Book, keyboard, Mobile etc.

3. Examine if the following are true statements:

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

(ii) The cube can cast a shadow in the shape of a hexagon. (True) (Fig a&b)

a b c

reference videos : https://www.youtube.com/hashtag/netsof3dshapes

https://brainly.in/question/5586621

https://www.excellup.com/seventh_math/7_math_chapter_15_2.aspx

Notes Prepared by

Mrs. Shazida Begum Shaik

Secondary Boy’s section