Practicing with Maths Mela Class 4 Solutions Chapter 1 Shapes Around Us Question Answer NCERT Solutions improves a student’s confidence in the subject.
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 Pg 1)
Question 1.
Try to make a model of the buildings shown here using below.
(i) What parts of the building have you shown in your model (for example, roof, pillers, base etc.)?
(ii) Why did you select these parts?
(iii) What shapes will model these parts well?
(iv) How is your model similar to the picture of the real building?
(v) How is it different from the real building?
Answer:
(i) Roof, base, pillars and arches.
(ii) Because they are the most visible and important features of the building.
(iii) Pillars – Cylinders, Roof – Triangle/Cone, Base – Cuboid/Rectangle
(iv) It has a base, roof and pillars just like the original.
(v) It is smaller and made with blocks, not the actual materials.
Discussion Answer (NCERT Pg 1)
Question 2.
(i) What would happen if you removed one piece of your model?
(ii) Would the model still look like the original building?
(iii) In what ways could you make the model even better?
Answer:
(i) If one piece is removed, the model may not look like the original.
(ii) No, the model does not look like the original building.
(iii) We can use more accurate shapes and decorations to improve it.
Question 3.
Project Work (NCERT Pg 2)
(i) Do you think it looks like Qutub Minar?
(ii) What shape would you use if you made a model of the Qutub Minar? Why?
(iii) How many such shapes will you use?
Answer:
(i) Yes, it has a tall, tapering cylindrical shape like Qutub Minar.
(ii) A cylinder on base and cone on top, as Qutub Minar is cylindrical and tapers.
(iii) 1 cone +1 or more cylinders (for each storey).
Question 4.
What is common to all of these bricks?
Answer:
They all have rectangular faces and flat surfaces.
Craft (NCERT Pg 3-4)
Question 5.
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.
Answer:
Do yourself
Question 6.
Use the nets given at the end of the book to make the models shown below.
(i) What shape of face is common to all the prisms?
(ii) What other shapes do these prisms have?
(iii) How many such faces each?
(iv) What shape of face is common to all pyramids?
(v) All the triangular faces meet at ………… point.
(vi) Identify any other shape in each of the pyramids.
(vii) Is a cube also a prism?
(viii) What is the difference between prism and pyramid? Discuss.
Answer:
(i) The common shape of the face in all prisms is a rectangle. Each prism has rectangular lateral faces and identical top and bottom faces (the bases).
(ii) Apart from rectangles, the base shapes of prisms vary
- Triangular prism → Triangle base
- Square prism (Cube) → Square base
- Hexagonal prism → Hexagon base
Each prism has 2 bases of the same shape, connected by rectangular faces.
(iii) From the given prism figures
| Prism type | Base shape | Number of faces | Rectangular faces |
| Triangular prism | Triangle | 5 | 3 |
| Square prism | Square | 6 | 4 |
| Hexagonal prism | Hexagon | 8 | 6 |
So, the number of rectangular lateral faces
= Number of sides in the base pyramids
(iv) All pyramids have triangular faces that meet at the apex (top point). These triangular faces are the side faces of the pyramid.
(v) All the triangular faces meet at one point, called the apex.
(vi) Other shapes in the given pyramids are given below.
The base of each pyramid can vary
- Square pyramid → Square base
- Triangular pyramid (Tetrahedron) → Triangle base
- Pentagonal pyramid → Pentagon base
So, the other shapes are triangle, square and pentagon.
But the side faces are always triangles.
(vii) Yes, a cube is a square prism.
(viii) Prism has two identical parallel bases. Pyramid has one base, triangular faces meet at apex.
Question 7.
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?
The relationship between the number of faces ( F), edges ( E ) and corners (V) is (F) + (V) – (E) = 2.
Question 8.
Sort 3D shapes by the number of flat faces. Write their names here.
| Number of faces | 1 flat face |
2 flat faces |
3 flat faces |
4 flat faces |
5 flat faces |
6 flat faces |
7 flat faces |
| Name of the shape |
Answer:
Question 9.
Can you construct a 3D shape with 3 flat faces?
Answer:
Do yourself
Question 10.
Sort 3D shapes by the number of straight edges. Write their names here.
| Now sort 3D shapes by the number of straight edges. names here. | Write their | |||
| Number of edges | 6 straight edges | 8 straight edges | 9 straight edges | 12 straight edges |
| Name of the shape | ||||
Answer:
Let Us Observe (NCERT Pg 5)
Question 11.
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
(i) face numbered 2 ?
(ii) face numbered 3 ?
(iii) face numbered 4 ?
Answer:
(i) Face numbered 2 → 5
(ii) Face numbered 3 → 4
(iii) Face numbered 4 → 3
Question 12.
(i) Which faces have common edges with the face numbered 1 ?
(ii) Which faces has no common edge with the face numbered 1 ?
Answer:
(i) Faces 2, 3, 4, and 5
(ii) Face 6
Question 13.
Look at three different views of the same cube.
(i) What colour is the face that is opposite to the red face?
(ii) What colour is the face that is opposite to the yellow face?
Answer:
(i) Opposite of red → purple
(ii) Opposite of yellow → green
Question 14.
Follow these instructions for the shapes along the border.
(i) Colour all shapes with a rectangular face in red.
(ii) Draw a smiley on shapes with a triangular face.
(iii) Draw a star on shapes with a curved face.
(iv) Colour all shapes with no corner in blue.
(v) Circle the shapes that have the same opposite faces.
Answer:
Do yourself
Sorting 3D Shapes (NCERT Pg 6)
Question 15.
Write the names of 3D shapes in the correct places.
Answer:
(NCERT Pg 7)
Question 16.
In which circle did you write triangular prism and rectangular pyramid?
Answer:
In the overlapping part of the two circles (in question 3 on page 6).
Question 17.
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:
You can make a Venn diagram with these two categories
(i) Circle A – Shapes with curved faces
- Sphere
- Cylinder
- Cone
(ii) Circle B – Shapes with flat faces
- Cube
- Cuboid
- Square pyramid
- Triangular prism
- Rectangular pyramid
(iii) Overlapping area (both flat and curved faces)
Cylinder and Cone (both have 1 or more flat faces + curved face)
So final classification
| Curved faces only | Flat faces only | Both |
| Sphere | Cube | Cone |
| Cuboid | Cylinder | |
| Triangular prism | ||
| Square pyramid | ||
| Rectangular pyramid |
Build with Cubes (NCERT Pg 7)
Question 18.
Build these models with the cubes from the Jaadui Pitara Kit or any other similar material.
Ansswer:
Do yourself
Cube Towers (NCERT Pg 7)
Question 19.
How many cubes are there in each of these cube towers?
Answer:
Left tower
- Number of cubes at bottom layer =16 cubes
- Number of cubes at second layer =9 cubes
- Number of cubes at third layer =4 cubes
- Number of cubes at top = 1 cube
- Total number of cubes = 30 cubes
Right tower ( X shape)
There are 15 cubes in each stair type wall.
So, number of cubes in 4 stair type wall = 4×15 =60
Number of cubes in middle row =6
So, total cube in tower = 60+6 =66
Drawing Cubes on a Triangular Dot Paper (NCERT Pg 8)
Question 20.
Can you complete the following cubes?
Answer:
Do yourself
Question 21.
Match the pictures to the descriptions and name the shapes
(i) I have 5 faces and 5 corners. I have 8 edges. One of my faces is a square and 4 of my faces are triangles’ ……….
(ii) ‘ I have 1 flat face, 1 curved face and 1 edge’ ………..
(iii) ‘I have 1 curved face. I have no edges or corners’ ………..
(iv) ‘I have 2 flat faces, 1 curved face and 2 edges. I have no corners’ ………..
(v) ‘I have 5 faces, 6 corners, 9 edges and 2 of my faces are triangles’ ………..
(vi) ‘I have 6 faces, 12 edges and 8 corners’ ………..
Answer:
(i) Square pyramid
(ii) Cone
(iii) Sphere
(iv) Cylinder
(v) Triangular prism
(vi) Cuboid (or Cube)
Question 22.
Each one is different. How? Discuss.
Answer:
Each shape is different based on number and type of faces (flat or curved), number of edges and number of corners/vertices e.g.
- Sphere has no flat faces or corners.
- Cube has only flat square faces.
- Cone has one curved and one flat face.
- Pyramid has different type of flate faces.
(NCERT Pg 9)
Question 23.
Match the following nets to the appropriate solids given below.
Answer:
(1) → (b) → Triangular pyramid
(2) → (d) → Cylinder
(3) → (a) → Cuboid
(4) → (c) → Square pyramid
Question 24.
Which of these nets can be folded to make a solid of the kind given below?
Answer:
(a) → (i) matches the yellow cuboid
(b) → (ii) matches the orange cylinder
(c) → (iii) matches the red triangular pyramid
(d) → (iv) matches the pink square pyramid
So, all nets ( A, B, C, D) can be folded to make the respective solids shown below them.
Question 25.
Nitesh cuts up a net on the folds. Here are its pieces.
Which solid has the above pieces in its net?
Answer:
From the given triangular pieces and the pentagonal base, 5 triangles +1 pentagonal base = Net of a pentagonal pyramid
Correct option-(d)
Let Us Do (NCERT Pg 10-11)
Question 26.
Mark the angles in the following pictures
Answer:
Question 27.
Where do you see angles in the classroom? Give few examples.
Answer:
Blackboard, Duster, Chair, Table etc.
Right Angles (NCERT Pg 11)
Question 28.
Let’s make a right angle with a piece of paper as shown.
Answer:
Do yourself
Question 29.
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:
Question 30
Check for right angles in a book, window and any other object. Write names of objects where you find right angles.
Answer:
Some classroom-related examples are Book,
Blackboard/Whiteboard,
Notebook pages,
Window panes,
Table corners,
Eraser,
Geometry box, … etc.
Let Us Do (NCERT Pg 12)
Question 31.
Draw some right angles on the dot grid.
Answer:
Do yourself
Acute and Obtuse Angles (NCERT Pg 12)
Question 32.
Acute angles are less than a right angle.
Obtuse angles are more than a right angle.
(i) Name some objects from your classroom which have an acute angle.
(ii) Name some objects from your classroom which have an obtuse angle.
(iii) Identify all angles in the following letters V, A, Z.
Answer:
(i) The sharp corners of a scissors blade, the tip of a pencil, the angle between the hands of a clock at 10:10 and corners of a triangle-shaped scale etc.
(ii) The angle between the pages of a slightly open book, the backrest and seat of a reclined chair, the hands of a clock at 2:10 and a protractor showing 120°
(iii) V has acute angles.
A has obtuse angle.
Z has acute angle.
Let Us DO (NCERT Pg 13)
Question 33.
(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.
(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.
Answer:
Do yourself
Question 34.
In the figures given below, mark the acute angles in red, right angles in green and obtuse angles in blue.
Answer:
Shapes with Straws (NCERT Pg 14)
Question 35.
(i) Make a triangle with straws of different sizes and clay/plasticine.
(ii) Does the shape of the triangle change if we gently push one of its sides? Yes or No.
(iii) Trace the triangle made with the straws in your notebook.
(iv) What kinds of angles does a triangle have?
Answer:
(i) Do yourself
(ii) No, the triangle does not change shape easily.
A triangle is a rigid shape-pushing one side does not change its overall shape.
(iii) Do yourself
(iv) A triangle can have all acute angles, one right angle and one obtuse angle.
Question 36.
(i) Make a rectangular shape with using straws and clay.
(ii) What kinds of angles do you see in the rectangle?
(iii) Does the shape of the rectangle change if we gently push one of its sides? Yes/No
(iv) What has happened to the angles of the new shape? Are they still right angles? What types of angles have been formed?
(v) Similarly, push one side of a square. Are they still right angles? What types of angles have been formed?
(vi) How are the angles of triangles and rectangles similar or different?
Answer:
(i) Do yourself
(ii) A rectangle has four right angles (90°).
(iii) Yes, the rectangle bends and changes shape.
(iv) The angles of the new shape has changed. The angles are no longer right angles. Some become acute and some become obtuse.
(v) No, they are not right angles now. The square bends like the rectangle-forming acute and obtuse angles.
(vi) A triangle stays in shape-its angles remain stable (more rigid) and triangle has different type of angles like acute angle, obtuse angle and right angle.
A rectangle changes angles when pushed-it is less rigid and rectangle has only right angles.
(NCERT Pg 15)
Question 37.
(i) Use the dot grid given below to draw several three and four-sided shapes. Circle the shapes that have one or more right angles.
(ii) What shapes did you make?
(iii) How many shapes have you made with
(a) 1 right angle
(b) 2 right angles
(c) 3 right angles
(d) All right angles
(iv) Here are some 4 -sided shapes.
In what ways are rectangle and square different from these other shapes?
Answer:
(i) Do yourself
(ii) Do yourself
(iii) Do yourself
(iv)
- A rectangle and a square have 4 right angles.
- A square has all sides equal, while a rectangle has opposite sides equal.
- Other quadrilaterals like rhombus, parallelogram and kite may which are shown in figures not have right angles or equal angles.
(NCERT Pg 16)
Question 38.
(i) Try to make this 5-sided shape with all sides equal (pentagon).
(ii) Are these right angles?
(iii) Does the shape of the pentagon change if we gently push one of its sides? Yes/No
(iv) How does this change the angles?
(v) Can you make a circle using straws?
(vi) Look at the picture. The lengths of the straws in this picture are …………………
(vii) What will happen if we take straws of unequal lengths?
Answer:
(i) Do yourself
(ii) No, the angles in a regular pentagon are not right angles (they are about 108°).
(iii) Yes, it can change shape slightly unless it is fixed or supported.
(iv) Some angles become acute (less than 90° and others become obtuse (more than 90°).
(v) No, because straws are straight. A circle has a curved line.
(vi) The length of the straws in this picture are equal.
(vii) The shape will not be a perfect circle. It will be uneven.
Amazing Circles (NCERT Pg 17)
Question 39.
(i) The length of all the creases are …………..
(ii) These creases are called of the circle.
(iii) Discuss where the centre is. Do you notice that all the diameters pass through the centre?
(iv) Measure the length of the creases from the centre to the border of the circle. This is called the \qquad
(v) Discuss if there is any relationship between the radius and the diameter of a circle.
Answer:
(i) Equal
(ii) Diameters
(iii) Yes, the centre is the common point through which all diameters pass.
(iv) Radius
(v) Yes; Diameter =2 × Radius
or Radius = Diameter ÷ 2
Let Us Do (NCERT Pg 18)
Question 40.
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.
Answer:
The length of the diameter is double of the length of radius.
Question 41.
A circle can be made easily using a compass. Ask your teacher to help you use a compass. Make the following design.
Answer:
Do yourself
Question 42.
Look at the carpet design. A beautiful circle, right?
Mark the centre, radius and the diameter of the circular design with any colour of your choice.
Answer:
Do yourself
(NCERT Pg 19)
Question 43.
Look at the wheels.
(i) All wheels look like ……….
(ii) Name the wheel with the
(a) longest radius
(b) shortest radius
(c) longest diameter
(d) shortest diameter
Answer:
(i) Circles
(ii) (a) Wheel B (visually appears longest)
(b) Wheel D (visually appears shortest)
(c) Wheel B (same as longest radius)
(d) Wheel D (same as shortest radius)
Puzzling Shapes (NCERT Pg 19-20)
Question 1.
Identify the hidden shapes and write their names.
Answer:
Some commonly hidden shapes could be
- Triangle
- Square
- Rectangle
- Circle
- Semicircle
- Pentagon
Question 2.
Draw 2 lines to divide the triangle into 1 square and 2 triangles.
Answer:
Do yourself
Question 3.
Draw 2 lines to divide the square into 3 triangles.
Answer:
Do yourself
Question 4.
Draw lines to show the cuts needed on the shapes in the left column to get the smaller shapes on the right.
Answer:
Do yourself
Card Game (NCERT Pg 20)
Question 5.
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:
Do yourself
Let Us Try (NCERT Pg 21-23)
Question 1.
(i) Squiggly, the spider, likes to make webs in different shapes. One day the begins to make triangular webs.
(a) How many triangles are in her web?
(b) Can she begin at point A and reach back to the same point without walking on any wall more than once?
(c) Trace and show squiggly’s path.
(ii) Her brother, wiggly made a web using rectangles.
(a) How many rectangles can you see in his web?
(b) Can he begin at point A and leave from point B without walking on any wall more than once?
(c) Trace and show wiggly’s path.
Answer:
(i) (a) There are 10 triangles in the web. These triangles are CBD, AEF, CGE, DGF, CDG, EGF, ECF, EFD, CED and EFD.
(b) No, she cannot return to point A without walking on the same wall more than once.
Explanation This is similar to an Eulerian path. Since, more than two vertices have an odd number of connecting walls (edges), it is not possible to complete the circuit without repeating an edge.
(c) Do yourself
(ii) (a) There are 10 rectangles in the web. These rectangles are AIGH, JHKM, GFNE, KLMB, CNDE, JHLB, GFCD, JGKN, FHEM, IAMN, HGMN and KJEF.
(b) Yes
Explanation Wiggly can walk from A to B without repeating any wall because the number of vertices with odd degree is exactly 2 – this makes an Eulerian path possible.
Sample path trace Follow outer path → right→inner rectangles → reach B.
(c) Do yourself
Question 2.
Use 5 matchsticks to make 2 triangles.
Answer:
Do yourself
Question 3.
Move two of these matchsticks to form 4 triangles.
Answer:
Do yourself
Question 4.
Remove 4 of these matchsticks to leave only 3 triangles.
Answer:
Do yourself
Question 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:
Do yourself
Question 6
(i) Classify these shapes based on the number of angles.
(3 angles, 4 angles, 5 angles)
(ii) What relation do you notice between the number of sides and the number of angles?
Answer:
| Number of angles | Shapes (a-g) |
| 3 angles | b, d, f |
| 4 angles | a, c, g |
| 5 angles | e |
(ii) In any closed 2D polygon, the number of sides is always equal to the number of angles.
Question 7.
(i) Draw a 2D shape that has less than 5 angles.
(ii) Draw a 2D shape with more than 5 angles.
Answer:
(i) Do yourself
(ii) Do yourself
Question 8.
(i) Mark the right angles and write the number of right angles in each figure.
Which of the above shapes have only right angles?
(ii) Which of the above shapes have only right angles?
Answer:
(i) (a) 4
(b) 0
(c) 1
(d) 0
(e) 0
(f) 4
(ii) Shapes (i) and (iv) have only right angles.
Question 9.
Observe the following shapes.
Identify the shape that has
(i) 2 right angles, 1 acute and 1 obtuse angles ……..
(ii) 1 right, 2 obtuse and 1 acute angles …….
(iii) 2 obtuse and 2 acute angles ……..
(iv) 4 right angles ………
Answer:
(i) 2,7
(ii) 10
(iii) 3,5,8,9,11,13
(iv) 14