Students often refer to Maths Mela Class 4 Solutions Chapter 1 Shapes Around Us Question Answer NCERT Solutions to verify their answers.
Class 4 Maths Chapter 1 Shapes Around Us Question Answer Solutions
Shapes Around Us Class 4 Maths Solutions
Class 4 Maths Chapter 1 Solutions
Try to make a model of the buildings shown here using blocks.
Question 1.
What parts of the building have you shown in your model (for example, roof, pillars, base, etc.)?
Answer:
I have shown base, arches, pillars and roof of the building in my model:
Question 2.
Why did you select these parts?
Answer:
I have selected these parts because they form the main structure of the building.
Question 3.
What shapes will model these parts well?
Answer:
Squares, rectangles, semicircles, cuboids and cylinders are the shapes that model these parts well.
Question 4.
How is your model similar to the picture of the real building?
Answer:
The shapes of the different parts of my model are almost similar in the overall structure.
Question 5.
How is it different from the real building?
Answer:
My model is a miniature version of the real building, with significantly smaller dimensions. It is made up of simple geometric shapes rather than stone.
Discussion (Page 1)
What would happen if you removed one piece of your model?
Answer:
The model might become unstable or look incomplete.
Would the model still look like the original building?
Answer:
No, the model won’t look like the original building.
In what ways could you make the model even better?
Answer:
To make the model even better, I could paint it in colours that closely resemble the actual building.
Project Work (Page 2)
Do you think it looks like the Qutub Minar?
Answer:
No, it doesn’t look like the Qutub Minar.
What shape would you use if you made a model of the Qutub Minar? Why?
Answer:
I would use a cylindrical shape to make a model of the Qutub Minar because the actual structure is tall and round, similar to a cylinder.
How many such shapes will you use?
Answer:
I would use five cylindrical shapes to make different levels of the Qutub Minar.
Earlier, people made buildings with clay bricks, stone blocks or wood. Today we also use concrete blocks, hollow blocks, etc.
What is common to all of these bricks? ______
Answer:
Clearly, all of these bricks are cuboidal in shape.
Craft (Pages 3-4)
1. Make a sphere-like shape with paper strips.
Answer:
2. Use the nets given at the end of the book to make the models shown below.
Answer:
Is a cube also a prism?
Answer:
Yes, a cube is a special type of prism where all faces are squares and all edges are of equal length.
What is the difference between a prism and a pyramid? Discuss.
Answer:
A prism has two identical, parallel bases (which can be triangles, squares, hexagons, etc.) connected by rectangular faces.
A pyramid, on the other hand, has only one base (which can be a triangle, square, pentagon etc.), and all the other faces are triangles.
3. Now try to make the above shapes using straws and plasticine/ thread and fill in the table.
Answer:
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?
Answer:
(i) Cube/Square Prism: F + V – E = 6 + 8 – 12 = 14 – 12 = 2.
(ii) Cuboid/Rectangular Prism: F + V – E = 6 + 8 – 12 = 14 – 12 = 2.
(iii) Triangular Pyramid: F + V – E = 4 + 4 – 6 = 8 – 6 = 2.
(iv) Square Pyramid: F + V – E = 5 + 5 – 8 = 10 – 8 = 2.
(v) Triangular Prism: F + V – E = 5 + 6 – 9 = 11 – 9 = 2.
In each case, we note that F + V – E = 2.
Can you construct a 3D shape with 3 flat faces?
Answer:
No, it is impossible to construct 3D shape with 3 flat faces.
Let Us Observe (Page 5)
Question 1.
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 ? _____
Answer:
We know that numbers on opposite faces of a die always add up to 7 . Therefore:
| Face number | Calculation | Opposite number |
| 2 | 7 – 2 = 5 | 5 |
| 3 | 7 – 3 = 4 | 4 |
Question 2.
(a) Which faces have common edges with the face numbered 1 ?
(b) Which face has no common edge with the face numbered 1 ?
Answer:
(a) Faces having common edges with the face numbered 1 are 2, 3, 4 and 5.
(b) Faces having no common edges with the face numbered 1 is 6.
Question 3.
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? _____
Answer:
(a) Colour of face opposite to red face – Purple.
(b) Colour of face opposite to yellow face – Green.
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.
Answer:
Do yourself.
Sorting 3D Shapes (Pages 6-7)
Write the names of 3D shapes in the correct places.
In which circle did you write triangular prism and rectangular pyramid?
Answer:
Clearly, triangular prism and rectangular pyramid are written in circle 1(B), Circle 2(B) and intersection of circles 3(A) and 3(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”?
Answer:
Build with Cubes (Page 7)
Build these models with the cubes from the Jaadui Pitara Kit or any other similar material.
Cube Towers (Page 7)
How many cubes are there in each of these cube towers?
Answer:
There are 30 cubes in the first tower.
There are 66 cubes in the second tower.
Drawing Cubes on a Triangular Dot Paper (Pages 8-9)
Can you complete the following cubes?
Answer:
Yes, we can complete the given cubes:
1. 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 corners, and 9 edges, and 2 of my faces are triangles _____.
f) I have 6 faces, 12 edges, and 8 corners _____.
Answer:
2. Each one is different. How? Discuss.
Answer:
All these shapes are different from each other due to their difference in properties such as number of faces, edges, and corners.
(i) Sphere:
Faces: 1 curved surface, Edges: 0, Corners: 0
(ii) Cone:
Faces: 1 curved surface and 1 circular base, Edges: 1, Corners: 1
(iii) Sphere Pyramid:
Faces: 4 triangular faces and 1 square base, Edges: 8, Corners: 5
(iv) Cube:
Faces: 6 square faces, Edges: 12, Corners: 8
(v) Cuboid:
Faces: 6 rectangular faces, Edges: 12, Corners: 8
3. Match the following nets to the appropriate solids given below.
Answer:
4. Which of these nets can be folded to make a solid of the kind given below?
Answer:
Of these, B and D can be folded to form a solid like the one given below.
5. Nitesh cuts up a net on the folds. Here are its pieces.
Which solid has the above pieces in its net?
Answer:
Option (d) has a pentagon and five triangles in its shape.
When Lines Meet (Page 10)
How many angles are there in this boat drawing?
Answer:
10
Let Us Do (Pages 10-11)
1. Mark the angles in the following pictures.
Answer:
2. Where do you see angles in the classroom? Give a few examples.
Answer:
Angles can be seen in many places around the classroom. They are present in the doors, cupboards, corners of desks, chairs, tables, windows, and whiteboard.
Right Angles (Page 11)
Identify the angles that you think are right angles and circle them in the dot grid given below. Check using your right angle checker.
Answer:
Check for right angles in a book, window, and any other object.
Write the names of objects where you find right angles.
_______________________________________
_______________________________________
Answer:
Right angles can be found in objects such as books, desks, windows, doors, chairs, blackboards, etc.
Let Us Do (Page 12)
1. Draw some right angles on the dot grid.
Answer:
Acute and Obtuse Angles (Page 12)
Name some objects from your classroom which have an acute angle.
Answer:
- Clock hands at 10:10.
- Slightly opened scissors.
- The sharpened tip of a pencil.
- The edges of a set square.
Name some objects from your classroom which have an obtuse angle.
Answer:
- Open door
- A tilted laptop screen.
- The angle between the minute and hour hands at 8:00 AM.
- An open notebook.
- Leaning chair.
Identify all angles in the following letters.
Answer:
Let Us Do (Page 13)
(a) Draw some acute angles on the top grid. Draw a line to make an acute angle using each given line in the bottom grid.
(b) Draw some obtuse angles on the top grid. Draw a line to make an obtuse angle using each given line in the bottom grid.
Answer:
2. In the figures given below, mark the acute angles in red, right angles in green, and obtuse angles in blue.
Answer:
Shapes with Straws (Pages 14-15)
Make a triangle with straws of different sizes and clay/plasticine.
Does the shape of the triangle change if we gently push one of its sides? Yes/No
Answer:
Yes
What kinds of angles does a triangle have?
Answer:
A triangle can have:
(i) All three acute angles.
(ii) One right angle and two acute angles.
(iii) One obtuse angle and two acute angles.
What kinds of angles do you see in the rectangle? _____
Answer:
A rectangle has 4 right angles.
Does the shape of the rectangle change if we gently push one of its sides? Yes/No
Answer:
Yes
What has happened to the angles of the new shape?
Answer:
The measure of the angles have changed.
Are they still right angles? What types of angles have been formed?
Answer:
No, the new shape doesn’t have right angles. Acute and obtuse angles have been formed.
Similarly, push one side of a square. Are they still right angles? What types of angles have been formed?
Answer:
The angles are no longer right angles. Two acute angles and two obtuse angles have been formed.
How are the angles of triangles and rectangles similar or different?
Answer:
Triangles maintain their shape when pushed, while rectangles deform. A rectangle always has four right angles, while a triangle can have different types of angles.
Use the dot grid given below to draw several three- and four-sided shapes. Circle the shapes that have one or more right angles.
Answer:
Discuss (Page 15)
What shapes did you make?
Answer:
I made three triangles, a square, a rectangle and a parallelogram.
How many shapes have you made with
(a) 1 right angle
(b) 2 right angles
(c) 3 right angles
(d) all right angles
Answer:
| Number of right angles | Number of shapes |
| 1 right angle | 2 |
| 2 right angles | 0 |
| 3 right angles | 0 |
| All right angles | 2 |
Here are some 4-sided shapes.
In what ways are rectangle and square different from these shapes?
Answer:
Rectangles and squares both have four right angles, whereas each of these shapes are formed by a combination of acute and obtuse angles.
Try to make this 5 -sided shape with all sides equal (Pentagon) (Page 16) Are these right angles?
Answer:
No
Does the shape of the pentagon change if we gently push one of its sides. Yes/No
Answer:
Yes
How does this change the angles?
Answer:
The pentagon shows a combination of acute and obtuse angles.
Can you make a circle using straws? (Page 16)
Look at the picture. The lengths of the straws in this picture are _____ (Equal/Unequal)
Answer:
Equal.
What will happen if we take straws of unequal lengths?
Answer:
A circle cannot be formed.
Let Us Make (Page 16)
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?
Answer:
A circle
Amazing Circles (Page 17)
1. The length of all the creases are equal. (Equal/Unequal)
2. These creases are called diameters of the circle.
3. Discuss where the centre is. Do you notice that all the diameters pass through the centre?
4. Measure the length of the creases from the center to the border of the circle. This is called the radius of the circle.
5. Discuss if there is any relationship between the radius and the diameter of a circle.
Let Us Do (Page 18)
The length of the diameter is double (half/double) of the length of radius.
Look at the wheels. (Page 19)
All wheels look like circle.
Name the wheel with the
1. longest radius B
2. shortest radius D
3. longest diameter B
4. shortest diameter D
Puzzling Shapes (Pages 19-20)
1. Identify the hidden shapes and write their names.
Answer:
The hidden shapes are triangle, cylinder, circle, rectangle, square.
2. Draw 2 lines to divide the triangle into 1 square and 2 triangles.
Answer:
3. Draw 2 lines to divide the square into 3 triangles.
Answer:
4. Draw lines to show the cuts needed on the shapes in the left column to get the smaller shapes on the right.
Answer:
Card Game (Page 20)
Sort the 2D-shape cards given at the end of the book into three groups according to their sides.
Draw the sorted shapes in the space given below. Explain why you sorted your shapes in this way.
Answer:
Let Us Try (Pages 21-23)
1. 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.
Her brother, Wiggly made a web using rectangles. How many rectangles can you see in his 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 Wiggly’s path.
Answer:
Squiggly Spider:
Number of triangles in her web = 10.
Yes, she can begin at point A and reach back to the same point without walking on any wall more than once.
Squiggly’s path
= 1 → 2 → 3 → 4 → 8 → 9 → 6 → 11 → 10 → 7 → 5 → 12.
Wiggly Spider:
Number of rectangles in his web = 11.
Yes, he can begin at point A and leave from point B without walking on any wall more than once.
2. Use 5 matchsticks to make 2 triangles. Then draw it in the space provided.
Answer:
3. Move two of these matchsticks to form 4 triangles.
Answer:
4. Remove 4 of these matchsticks to leave only 3 triangles.
Answer:
5. Model challenge.
Can you make a model of solid shapes which has
(a) 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?
Answer:
(a) Cuboid (12 straws and 8 clay balls)
(b) Triangular prism (9 straws and 6 clay balls)
(c) Pentagonal prism (15 straws and 10 clay balls)
(d) Pentagonal pyramid (10 straws and 6 clay balls)
6. Classify these shapes based on the number of angles.
What relation do you notice between the number of sides and the number of angles?
Answer:
Shapes with 3 angles -b, d, f.
Shapes with four angles – a, c, g.
Shapes with five angles – e.
In the figure, the number of sides is equal to the number of angles.
7. Draw a 2D shape that has less than 5 angles.
Draw a 2D shape with more than 5 angles.
Answer:
8. Mark the right angles and write the number of right angles in each figure.
Which of the above shapes have only right angles?
Answer:
Angles of rectangle and square are only right angles.
9. Observe the following shapes.
Identify the shape that has:
Answer:
- 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.