NCERT Solutions for Class 4th Maths Chapter 1 A die, three views of a cube, and the shapes along the border — Let Us Observe
Book page 5 Updated on2026-09-19
Q1.
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?
The die in the book. Three of its faces can be seen: 1 in front, 5 on top and 3 on the right.
Answer
On a die, two opposite faces always add up to 7.
1 + 6 = 7 (this is the pair the book gives us)
a) 2 + 5 = 7 → opposite of 2 is 5
b) 3 + 4 = 7 → opposite of 3 is 4
c) 4 + 3 = 7 → opposite of 4 is 3
Why it happens: A die has 6 faces and the numbers 1 to 6 are
placed in pairs, one pair on each pair of opposite faces. The pairs are 1 and 6, 2 and
5, 3 and 4 — and each pair makes 7.
Check it yourself: Hold a die. Whichever face you press on the
table, the number on top will always be 7 minus the number below.
Q2.
Which faces have common edges with the face numbered 1? ............................
The die in the book. Three of its faces can be seen: 1 in front, 5 on top and 3 on the right.
Answer
The faces numbered 2, 3, 4 and 5.
The face 1 is a square, so it has 4 edges.
Each of those 4 edges is shared with one side face.
Those side faces carry 2, 3, 4 and 5.
Why it happens: Every face of a cube touches the four faces
around it. Only the face right behind it does not touch it at all.
Q3.
Which face has no common edge with the face numbered 1? ...........................
The die in the book. Three of its faces can be seen: 1 in front, 5 on top and 3 on the right.
Answer
The face numbered 6.
6 is the face opposite to 1.
Opposite faces of a cube are far apart — they never touch.
So they share no corner and no edge.
Why it happens: A cube has 6 faces. One face touches 4 of the
others along its 4 edges; that leaves exactly one face that it does not touch — the
one opposite it.
Q4.
Look at three different views of the same cube. a) What colour is the face that is opposite to the red face? ……………………
Three different views of the same cube, as printed in the book.
Answer
The face opposite the red face is purple.
How to find it: a face and its opposite face can never be seen together.
In view 1 the red face is seen with green and
orange. So neither of those is opposite to red.
In view 3 the red face is seen with blue and
yellow. So neither of those is opposite to red either.
The six colours are red, green, orange, purple, blue and yellow. Red has now been
seen with four of them, so the only colour left is purple.
Why it happens: Two opposite faces point in opposite
directions, so a picture of the cube can never show both at once.
Q5.
What colour is the face that is opposite to the yellow face? .......................…………..
Three different views of the same cube, as printed in the book.
Answer
The face opposite the yellow face is orange.
How to find it: pair off the colours that have already been matched.
Red goes with purple (found in the question before this one).
In view 3, yellow is seen with blue and red — so yellow is not opposite to either
of them.
Only green and orange are left for yellow. In view 1 the top is orange and the right
is green; in view 3 the top is red and the right is yellow. Turning the cube from view 1
to view 3 takes the orange face to the back, and yellow comes to the front on the right.
So yellow and orange are the pair.
Then the last pair must be green and blue.
red ↔ purple yellow ↔ orange green ↔ blue
Why it happens: A cube has exactly three pairs of opposite
faces. Once two pairs are known, the third pair is fixed — the two colours left over
must face each other.
Q6.
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.
The kinds of solid drawn along the border of the page.
Answer
Look at each object on the border, decide which solid it is, and then follow the
five instructions. This table does the deciding for you.
Object on the border
It is a
Red
Smiley
Star
Blue
Circle
die, Rubik’s cube
cube
yes
no
no
no
yes
eraser, gift box, matchbox
cuboid
yes
no
no
no
yes
cheese wedge, wooden wedge, cake slice
triangular prism
yes
yes
no
no
yes
tennis ball, football
sphere
no
no
yes
yes
no
tin, pencil box
cylinder
no
no
yes
yes
yes
ice-cream cone, party hat
cone
no
no
yes
no
no
the diamond-shaped solid
two pyramids joined
no
yes
no
no
no
The reason for each column
Red — a cube, a cuboid and a prism all have flat rectangular faces.
Smiley — only the wedge-shaped prisms and the pointed solids have
triangular faces.
Star — the ball, the tin and the cone are the ones with a curved face.
Blue — the ball and the tin have no corner at all. (The cone has one sharp
corner at the top, so it is not coloured blue.)
Circle — a cube, a cuboid, a prism and a cylinder each have two ends that
are exactly the same.
Why it happens: Each instruction asks about one feature — a
kind of face, a corner, or matching ends — so the same object can get more than one
mark.