NCERT Class 4 Mathematics (Maths Mela) Solutions
Chapter 1: Shapes Around Us
Students can use Class 4 Maths Solutions and Maths Mela NCERT Class 4 Maths Chapter 1 Shapes Around Us Question Answer Solutions to explore alternative problem-solving methods.
Class 4 Maths Chapter 1 Shapes Around Us Question Answer Solutions
Shapes Around Us Class 4 Maths Solutions
Class 4 Maths Chapter 1 Solutions
NCERT Textbook Page 1
Try to make a model of the buildings shown here using blocks.
What parts of the building have you shown in your model
(for example, roof, pillars, base, etc.)?
Why did you select these parts?
What shapes will model these parts well?______________
How is your model similar to the picture of the real building? __________________
How is it different from the real building? ______________
Solution:
Do it yourself.
NCERT Textbook Pages 3-4
Craft
Make a sphere-like shape with paper strips.
Diksha has folded open and flattened a box to see what an open box looks like. This is called the net of the box. If you fold along the dotted lines, you will get the box back.
Solution:
Do it yourself.
Use the nets given at the end of the book to make the models shown below.
Prisms | Pyramids |
What shape of face is common to all the prisms? _________________ | What shape of face is common to all the pyramids? _______________ |
What other shapes do these prisms have? _________________ | All the triangular faces meet at _________________ point. |
How many such faces each? | Identify any other shape in each of the pyramids _________________ |
Is a cube also a prism?
What is the difference between a prism and a pyramid? Discuss.
What shape of face is common to all the prisms?
Solution:
All the prisms have rectangular faces. So, the shape of the face that is common to all the prisms is rectangle.
What other shapes do these prisms have?
Solution:
The prisms have triangle, hexagon and square as other shapes.
How many such faces each?
Solution:
A triangular prism has 2 triangular faces, a hexagonal prism has 2 ‘hexagonal faces and a square prism has 2 square faces which are identical and opposite to each other.
What shape of face common to all the pyramids?
Solution:
All the pyramids have triangular faces. So, the shape of the face common to all the pyramids is triangle.
All the triangular faces meet at point.
Solution:
All the triangular faces meet at a common point.
Identify any other shape in each of the pyramids.
Solution:
A triangular pyramid has only triangular faces, a pentagonal pyramid has a pentagonal face and a square pyramid has a square face.
Is a cube also a prism?
Solution:
A cube is a special type of square prism with 6 square faces.
What is the difference between a prism and a pyramid? Discuss.
Solution:
A prism has two identical bases while a pyramid has one base. Also, a prism has all rectangular or parallelogram-shaped side faces while a pyramid has all triangular side faces.
Now try to make the above shapes using straws and plasticine/thread and fill in the table.
Identify any relationship that you may find between the number of faces (F), edges (E), and corners (V). Calculate F+V–E in each case. What do you notice?
Can you construct a 3D shape with 3 flat faces?
Solution:
Hence, we observe that number of faces (F) + number of corners (V) – number of edges (E) = 2
No! We cannot construct a 3D shape with 3 flat faces.
NCERT Textbook Page 5
Let Us Observe
Take a die. Look at the face that has number 1. The face numbered 6 is opposite to the face numbered 1.
What is the face opposite to the
(a) face numbered 2?
(b) face numbered 3?
(c) face numbered 4?
Solution:
(a) A standard dice is designed so that the numbers on opposite faces always add up to 7.
Since, 7 – 2 = 5, the opposite of face numbered 2 is face numbered 5.
(b) Since, 7 – 3 = 4, the opposite of face numbered 3 is face numbered 4.
(c) Since, 7 – 4 = 3, the opposite of face numbered 4 is face numbered 3.
(a) Which faces have common edges with the face numbered 1?
(b) Which face has no common edge with face numbered 1?
Solution:
(a) Each face has common edges with all the other faces except the face opposite of it. So, the faces numbered 2, 3, 4, and 5 have common edges with the face numbered 1.
(b) The face opposite to the face numbered 1 is the face numbered 6. Therefore, face numbered 6 has no common edges with the face numbered 1.
Look at three different views of the same cube.
(a) What colour is the face that is opposite to the red face?
(b) What colour is the face that is opposite to the yellow face?
Solution:
(a) Purple face is opposite to the red face.
(b) Orange face is opposite to the yellow face.
Follow these instructions for the shapes along the border.
1. Colour all shapes with a rectangular face in red.
2. Draw a smiley on shapes with a triangular face.
3. Draw a star on shapes with a curved face.
4. Colour all shapes with no corner in blue.
5. Circle the shapes that have the same opposite faces.
Solution:
Do it yourself.
NCERT Textbook Page 6-7
Sorting 3D Shapes
Write the names of 3D shapes in the correct places.
In which circle did you write triangular prism and rectangular pyramid?
Solution:
In the region common to both circles A and B.
Let us sort shapes in another way.
Using circles like those on the previous page, can you sort shapes into the categories “Shapes with curved faces” and “Shapes with flat faces”?
Solution:
NCERT Textbook Page 7
Cube Towers
How many cubes are in each of these cube towers?
Solution:
- There are 30 cubes in the first tower.
- There are 66 cubes in the second tower.
NCERT Textbook Pages 8-9
Drawing Cubes on a Triangular Dot Paper
Can you complete the following cubes?
Solution:
Yes, it can be completed as shown above.
Match the pictures to the descriptions and name the shapes.
(a) I have 5 faces and 5 corners. I have 8 edges, 1 of my faces is a square and 4 of my faces are triangles ______________
(b) I have 1 flat face, 1 curved face and 1 edge ______________
(c) I have 1 curved face. I have no edges or corners ______________
(d) I have 2 flat faces, 1 curved face and 2 edges. I have no corners ______________
(e) I have 5 faces, 6 comers and 9 edges, 2 of my faces are triangles ______________
(f) I have 6 faces, 12 edges and 8 corners ______________
Solution:
(a) I have 5 faces and 5 corners. I have 8 edges, 1 of my faces is a square and 4 of my faces are triangles Square pyramid
(b) I have 1 flat face, 1 curved face and 1 edge Cone
(c) I have 1 curved face. I have no edges or corners Sphere
(d) I have 2 flat faces, 1 curved face and 2 edges. I have no corners Cylinder
(e) I have 5 faces, 6 comers and 9 edges, 2 of my faces are triangles Triangular prism
(f) I have 6 faces, 12 edges and 8 corners Cube/Cuboid
Each one is different. How? Discuss.
Solution:
- The sphere has 1 curved face and no flat face.
- The cone has 1 flat face and 1 curved face.
- The triangular pyramid has 4 triangular faces.
- The cube has all the six square faces.
- The cuboid has all the 6 rectangular faces.
So, each one of the given solids is different in terms of shape of the faces.
Match the following nets to the appropriate solids given below-
Solution:
(1)-(6),
(2)-(d),
(3)-(a),
(4)-(c).
Which of the nets can be folded to make a solid of the kind given below.
Solution:
Among the given nets, only B and D can be folded to make a solid of the kind given just below them.
Nitesh cuts up a net on the folds. Here are its pieces.
Which solid has the above pieces in its net?
Solution:
Nitesh cuts up 5 triangles and 1 pentagon. It can be the pieces of the nets of a pentagonal pyramid with a pentagon as a base and 5 triangular faces that meet at one point. Therefore, the correct solid is d.
NCERT Textbook Pages 10-11
When Lines Meet
How many angles are there in this boat drawing?
Solution:
There are 10 angles in the boat drawing.
Let Us Do
Mark the angles on the following pictures.
Solution:
Where do you see angles in the classroom? Give a few examples.
Solution:
Do it yourself.
Right Angles
Identify the angles that you think are right angles and circle them in the dot grid given below. Check using your right angles checker.
Solution:
Check for right angles in a book, window, and any other object. Write the names of objects where you find right angles.
Solution:
Do it yourself.
NCERT Textbook Page 12
Let Us Do
Draw some right angles on the dot grid.
Solution:
Acute and Obtuse Angles
Name some objects from your classroom which have an acute angle.
Solution:
Do it yourself
Name some objects from your classroom which have an obtuse angle.
Solution:
Do it yourself
Identify all angles in the following letters.
Solution:
NCERT Textbook Page 13
Let Us Do
(i) Draw some acute angles on the top grid. Draw a line to make an acute angle using each given line in the bottom grid.
Solution:
Following are drawings of some acute angles.
(ii) Draw some obtuse angles on the top grid. Draw a line to make an obtuse angle using each given line in the bottom grid.
Solution:
Following are drawings of some obtuse angles.
In the figures given below, mark the acute angles in red, right angles in green, obtuse angles in blue.
Solution:
Do it yourself.
NCERT Textbook Pages 14-16
Shapes with Straws
What kinds of angles does a triangle have?
Solution:
A triangle can have acute, obtuse or right angle.
Make a rectangular shape with straws and clay.
What kinds of angles do you see in the rectangle?
Solution:
A rectangle has four right angles.
Does the shape of the rectangle change if we gently push one of its sides?
Solution:
Yes
Use the dot grid given below to draw several three and four-sided shapes. Circle the shapes that have one or more right angles.
Solution:
Do it yourself
Here are some 4-sided shapes. In what ways are the rectangle and square different from these shapes?
Solution:
Rectangles and squares have all the corners as square corners while the given shapes have not square corners.
Try to make this 5-sided shape with all sides equal (Pentagon)
Are these right angles?
Solution:
No.
Does the shape of the pentagon change if we gently push one of its sides?
Solution:
Yes
How does this changes the angles?
Solution:
Do it yourself.
Can you make a circle using straws?
Look at the picture. The lengths of the straws in this picture are ______________
Solution:
Equal
What will happen if we take straws of unequal lengths?
Solution:
A circle cannot be formed.
Let Us Make
Can you use a scale to draw a circular shape? Let us see. Mark a point A.
Draw many points that are at an equal distance from point A.
Connect the dots freehand. What do you get? …………….
The point A is the centre and the line from the centre to the border of the circle is the radius.
Solution:
Do it yourself
NCERT Textbook Page 17
Amazing Circles
Take a piece of circular paper.
b) Fold your paper in half and crease it well.
c) Open the fold and measure the length of the crease using a thread.
d) Fold your paper in half in a different way and crease it well.
e) Open the fold and measure the length of the crease again.
f) Fold it again in half in a different way and crease it well.
g) Open the fold, measure the length of the crease.
1. The length of all the creases are ___________. (Equal/Unequal)
These creases are called ___________ of the circle.
Discuss where the centre is. Do you notice that all the diameters pass through the centre?
Measure the length of the creases from the center to the border of the circle. This is called the ___________ of the circle.
Discuss if there is any relationship between the radius and the diameter of a circle.
Look Pages 18-19
Let Us Do
Fold the circular paper in half.
Fold this half again in half.
The length of the diameter is ___________ (half/double) of the length of radius.
Solution:
The length of the diameter is double of the length of radius.
Look at the wheels
Solution:
All the wheels look like a circle
Name the wheel with the
1. longest radius ………………….
2. shortest radius ………………….
3. longest diameter ………………….
4. shortest diameter ………………….
Solution:
1. longest radius wheel B
2. shortest radius wheel D
3. longest diameter wheel B
4. shortest diameter wheel D
NCERT Textbook Pages 19-20
Puzzling Shapes
Identify the hidden shapes and write their names.
Solution:
The hidden shapes are triangle, square, rectangle, circle, and cylinder.
Draw 2 lines to divide the triangle into 1 square and 2 triangles.
Solution:
Draw 2 lines to divide the square into 3 triangles.
Solution:
Draw lines to show the cuts needed on the shapes in the left column to get the smaller shapes on the right.
Solution:
NCERT Textbook Page 21
Let Us Try
Squiggly spiders
Squiggly, the spider, likes to make webs in different shapes. One day she begins to make triangular webs.
How many triangles are in her web?
She likes to take a walk each morning and check if the walls of her web are strong.
Can she begin at point A and reach back to the same point without walking on any wall more than once?
Trace and show Squiggly’s path.
Solution:
Yes, Squiggly can begin at point A and reach back to the same point without walking on any wall more than once by following the order of the walls as shown.
Her brother, Wiggly made a web using rectangles. How many rectangles can you see in his web?
Solution:
There are 12 rectangles in Wiggly’s web.
He likes to take a walk at the end of each day and check if the walls of his web are strong. Can he begin at point A and leave from point B without walking on any wall more than once?
Trace and show Wigggly’s path.
Solution:
No, Wiggly cannot start from A and leave from B without walking on any walls more than once and also go through all the walls.
Use 5 matchsticks to draw 2 triangles.
Solution:
Move any two of these matchsticks to form 4 triangles.
Solution:
Remove 4 of these matchsticks to leave only _________
Solution:
Model challenge.
Can you make a model of solid shapes which has _________
(а) 12 straws and 8 clay balls?
(b) 9 straws and 6 clay balls?
(c) 15 straws and 10 clay balls?
(d) 10 straws and 6 clay balls?
Solution:
Classify these shapes based on the number of angles.
Solution:
What relation do you notice between the number of sides and the number of angles?
Solution:
In the figure, the number of sides is equal to the number of angles.
Draw a 2D shape which has less than 5 angles.
Solution:
Following is a 2D shape having only 4 angles.
Draw a 2D shape with more than 5 angles.
Solution:
Following is a 2D shape having 6 angles.
Mark the right angles and write the number of right angles in each figure.
Which of the above shapes have only right angles?
Solution:
The first and the last shapes in the given figure have only right angles.
Identify the shape that has:
Identify the shape that has:
- 2 right angles, 1 acute, and 1 obtuse angle ______________.
- 1 right, 2 obtuse, and 1 acute angle ___________.
- 2 obtuse, and 2 acute angles _____________.
- 4 right angles ____________.
- 2 right angles, 1 acute, and 1 obtuse angle 2, 7
- 1 right, 2 obtuse, and 1 acute angle 10
- 2 obtuse, and 2 acute angles 3, 5, 8, 9,11, 13
- 4 right angles 4, 6, 12, 14
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