NCERT Solutions Class 3 Maths Chapter 2 Toy Joy

F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T

+ ×
C L A S S 3 · M AT H S

NCERT Solutions

Chapter 2: Toy Joy

NCERT Textbook — Maths Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

9 – 15 10 37 English

Every question Step by step Exam ready
Activities, in-text questions The working shown, not Written to match how
and all exercises. just the final answer. marks are awarded.

Solutions, notes, sample papers & more at 45 pages

l h h e A aS m · NCERT So ut ons
gl e l i

C L A SS 3 · M AT H S · M AT H S M E L A
NCERT So ut ons — C apt r 2: Toy Joy
l i h e

This chapter turns a toy shop into a shape lesson. Old boxes, bottles, balls and party caps become the cube,
cuboid, cylinder, sphere and cone. You count them, join them and build with them.

T E XT B OOK B OOK PAGE S
Ma h Mela Cla
t s ss 3 9  15

S EC T I ONS QU E ST I ONS
10 37

M EDI UM
English

Let us Do — Page 9
Faces on old boxes, and Jayaʼs rocket

Q1 Wha did
t you a a
dr w on their f ces?

O oxes, a bottle and a paper cone with animal faces drawn on them.
ld b

Sample answer: I drew a puppy face on a bottle (cylinder), a pig face on a box (cube), a cat
face on a long box (cuboid) and a bird face on a paper cone.

− Exp anat on
l i

You can draw any animal or bird face you like. The faces above are the ones the children in
the book made.

Page 1 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Why A a a: fl t f ce is easy to draw on. A curved face bends, so the face you draw
on it looks round.

Try This: Draw a lion on a cube and an owl on a cone. Say the shape name
each time.

Q2 Ja a i b ildi g a cke
y s u n ro twt a
i h different sh pes. Wha ha e ha he ed?
ts p s ss us

Jaya s ro
ʼ t rawn simply. The blocks stand just as they do in the book.
cke , d

Jaya has used 4 kinds of shapes: cone, cube, cylinder and cuboid.
Con — the pink tip at the top.
e

Cu — the purple block and the blue block.
be

Page 2 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Cy nli de r
he big orange block.
—t

Cu ob id — the flat blocks around the base.

− Exp anat on
l i

Why A : cylinder is wide and steady, so it holds the tower up. A cone makes a
pointed nose, just like a real rocket.

Page 3 of 45

as e
l h h e

a g l A aS m · NCERT So ut ons
gl e l i

How many of each? Cube: Cuboid: Cone: Cylinder: .com
sem
Q3 _______ _______ _______ _______

m a
em . co agl
g l as
a

co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g

co m
m .
m as e
.co a g l
se m
a
Jaya s ro t rawn simply. The blocks stand just as they do in the book.
g l
ʼ cke , d

a
se m
com g l a
m . a
ase
Cube: 2 (purple, blue) agl
Cuboid: 4 (yellow, green, red, light blue)
co m
m .
as e
com 1 (orange)
Cone: 1 (pink)

.Cylinder: a g l
se m
g l a
a c
all, 2  4  1  1  8 bl ck . o s
m .
e
In

m a s
− Exp anat on
m . co agl
se
l i

Count each kind of bla
ock
a e by one and say its colour.
glon

co m
m .
m as e
.co

a g l Page 4 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Why T : he four flat blocks are all cuboids, even though their colours are

different. Colour does not change a shape.

Q4 Which ha e i be ee he ed c b id a d ell
s p s tw nt r u o n y ow cuboid?

Jaya s ro
ʼ t rawn simply. The blocks stand just as they do in the book.
cke , d

The orange cylinder is between the red cuboid and the yellow cuboid.
The yellow cuboid is on the left and the red cuboid is on the right.

Why B a a
: ‘ etweenʼ me ns with one thing on e ch side. Go from the yellow block to the
red block and you pass the orange cylinder.

Page 5 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q5 Which ha e i s p s on t a
he top of the or nge cylinder?

Jaya s ro
ʼ t rawn simply. The blocks stand just as they do in the book.
cke , d

The blue cube is on the top of the orange cylinder.
i
It s ts on t he flat top face of the cylinder.

− Exp anat on
l i

Look at the rocket from the bottom upwards: the orange cylinder, then the blue cube, then
the purple cube, then the pink cone.

Why T : he top of a cylinder is flat and round. A flat face can hold another block
without slipping.

Page 6 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q6 Which ha e i s p s under the pink cone?

Jaya s ro
ʼ t rawn simply. The blocks stand just as they do in the book.
cke , d

The purple cube is under the pink cone.
The cone is the top block. The small purple cube is just below it.

− Exp anat on
l i

Why A : cone has one flat round face at the bottom. That flat face rests neatly

a
on the fl t top of the cube. Below the purple cube is the blue cube.

Let us Do — Page 10

Page 7 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Making a house, and Devikaʼs toy engine

Q1 Collect objects to make a house. Name the shapes, and talk about their faces and
edges. Which a e aigh a d hich a e c
r str t n w r urv ed?

Sample answer: I collected a carton, a matchbox, a bottle, a paper cap and a ball.

OBJECT SHAPE ITS FACES ITS EDGES

Carton Cuboid 6 flat faces straight

Matchbox Cuboid 6 flat faces straight

Bottle Cylinder 2 flat and 1 curved round

Paper cap Cone 1 flat and 1 curved round

Ball Sphere only 1 curved face no edge

Straight edges: carton and matchbox. Curved edges: bottle and paper cap. The ball has no
edge.

− Exp anat on l i

Why A : n edge is the line where two f ces meet. a A ball has only one face, so it
has no edge at all.

Q2 Also, describe how the shapes have been arranged. What part of the shapes can you
see from dist nce? a a
Sample answer:
 A big carton (cuboid) at the bottom — the room.
 A cone on it — the roof.
 Two bottles (cylinders) at the sides — pillars.
From far away I can see only the faces turned towards me. The back and bottom faces are
hidden.

Page 8 of 45

as e
l h h e

a g l A aS m · NCERT So ut ons
gl e l i

co m
m.
− Exp anat on
l i

ild the housm acsan be the door e
c o g l
m.
e step by step and then say it aloud. A small cuboid in front
a
Bu

as
step.
e
a g l
Why T : he faces at the back and at the bottom are hidden behind the faces in

front, so you cannot see them.
co m
em . ag
g l as
a
Here is Devikaʼs toy engine. It has many parts. Count and fill. edocm
Q3
ellow cone(s) ________ grey cuboid(s) ________ blue cube(se)m
________ r
.c ylinder(s)

m a s
.co agl
________ y

se m
g l a
a
m a s
m .co agl
l a se
a g

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
aDglv a s toy n n
e ik ʼ e gi e, drawn simply, with all its parts.

co m
m .
A NSWm as e
.co
ER
a g l
se m
g l a
a 1 red cylinder — the boiler in front
c
m .
2 yellow cones — the funnels on top
m a s e
1 grey cuboid — the base
em . co agl
g l as
a
1 blue cube — the driver’s cabin

co m
m .
m as e
.co

a g l Page 9 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

In all, 1  2  1  1  5 s ap s
h e .

− Exp anat on
l i

Why T : he funnels are drawn with their points downwards. A cone is still a cone,
a
whichever w y you turn it. The black wheels are not asked for, so we do not
count them.

Let us Discuss — Page 10
More toys from the toy shop

Q1 Wha ha e a e ed i he e
ts p s r us nt s toys?

Four toys rom t f he toy shop: a mouse, a lollipop, a cat and a block toy.

Ev ry toy s ma
e i de b y o n n two or mor s ap s
j i i g e h e .

TOY SHAPES USED

Mouse cone (head) + cylinder (body)

Lollipop sphere (ball) + cylinder (stick)

Cat sphere (head) + cylinder (body)

Block toy cuboids (base plank, flat yellow top) + cubes (green, blue, purple)

Page 10 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Why A : cone gives a pointed nose. A cylinder makes a good round body. Toy
a a a
m kers pick the sh pe th t does the job.

Q2 Try to a aaa a
build such houses, towers, rockets, etc., using different sh pes v il ble round
you.

T
he four models Jaya made with her blocks.

Sample answer: I put a paper cone on a bottle to make a hut. I put a cone on a box to make a
house with a pointed roof. I kept the wide, flat box at the bottom.

− Exp anat on
l i

Jayaʼs four models:
 A cone on a cylinder — a small hut.
 A cone on a cube — a house with a pointed roof.
 Two cones on a flat cuboid — two huts side by side.
 Planks, cylinders, cubes and cones together — a big two-storey house.
Use matchboxes, chalk sticks, bottle caps and paper cones from your home.

Tip: Always put the wide, flat shape at the bottom. Then your tower will not fall.

Let us Play — Page 11

Page 11 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Construct and Describe

Q1 Construct and Describe. Sit in groups of four or five. n each group, one student
I

s a a a T
elects ny three sh pes nd puts them together. he student then describes the order
a a
of construction, nd the others build the s me without seeing the origin l one. ke a Ta
turns.

Example: The cylinder is of the cuboid. The cone is on the cylinder.

T
he example model: a cone on a cylinder, and the cylinder on a flat cuboid.

Sample answer: The cuboid is at the bottom. The cylinder is on the cuboid. The cone is on the
cylinder.

About the book: The example is printed as The cylinder is of the cuboid It should
“ .ˮ

a T
re d “ he cylinder is on the cuboid.ˮ

− Exp anat on
l i

Use words like on, under, beside and between. The others build without looking. Then
everyone compares the models. If they match, the description was clear.

Page 12 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Let us Do — Page 11
Question 1  shapes in the classroom

Q1 F n a a a a
i d the sh pes in the cl ssroom th t look like the following sh pes. And fill in the
a a
t ble with their n mes.

CUBE CONE
SPHERE CUBOID
CYLINDER

Sample answer: Write each classroom object under the shape it looks like.

SPHERE
CYLINDER CUBOID
CUBE CONE

chalk stick ball die duster birthday cap

water bottle globe small box book funnel

pencil marble alphabet block geometry box paper cone

drum orange carton table top ice-cream cone

Page 13 of 45

as e
l h h e

a g l A aS m · NCERT So ut ons
gl e l i

Why A and a shape need not be the same size. We only ask: does it choam
: thing ve the

m .
m ase
agl
a a and edges?
co
s me f ces

m .
as e
a g l
Q2 a Na e he ha e ha
( ) m t s p t t you find the most.

com
e m . ag
g l as
a
CUBE
co m
m.
CONE

m
SPHERE CUBOID
as e
.co
CYLINDER
a g l
se m
g l a
a
m a s
m.co agl
l a se
ag

co m
m .
m
o l a se
.c answ r Cu o a g
m
Samp
e ks the duster the geometry box the desk top the door and the blackboard are all cuboids
asoo
le e : b id.

agl
B , , , , .

se m
− Exp anat on
com g l a
.
l i

m a
Why C agl a ase
classroom t
:

hi g a e
a
uboids h ve fl t f ces.

n s
a Fla hi g
ade ha a
r m t
t t

t w y.
a
n s st ck, st nda and pack easily, so most

co m
m .
m e f e answer may be
Check it yourself: Count the cuboids in your own class Ysour
a
codiffe agl
.

m.
a friendʼs. Both can be right.
ase
r nt rom

a g l
.c
s e m
m a
e m . co agl
g l as
a

com
m .
m ase
.co

a g l Page 14 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q3 (b) Na e he ha e ha
m t s p t t you a
find the le st.

CUBE CONE
SPHERE CUBOID
CYLINDER

Sample answer: Cone.
I found only a birthday cap and a funnel. Some classrooms have no cone at all.

Why A : cone has a pointed tip. You cannot keep anything on a point, so very few

things are made as cones.

Page 15 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q4 (c) Na e he bjec
m t o ts t aa a a a
h t re m de up of more th n one sh pe.

CUBE CONE
SPHERE CUBOID
CYLINDER

Sample answer:
Pencil — a cylinder with a cone at the tip.
Water bottle — a big cylinder with a small cylinder cap.
Table — a cuboid top with cylinder legs.
Go l be — a sphere on a stand.

− Exp anat on
l i

Why Ea : ch part does its own job. The cone tip of a pencil writes, and the

cylinder body is easy to hold.

Let us Do — Page 12

Page 16 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Questions 2 and 3  marking and naming shapes

Q1 L k a he e ha e a d f ll
oo tt s s p s n o ow t he instructions below.
 Circle the cubes.
P a aa a
 ut tick g inst the sh pes th t re cones. aa
P a aa a aa
 ut cross g inst the sh pes th t re cylinders.
a a a
 Dr w box round the cuboids.

T he shapes printed in the book, drawn again.

Page 17 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

T he shapes with their marks: circle for cubes, tick for cones, cross for cylinders, box for cuboids.

There are 13 shapes. Each one gets its mark.

MARK SHAPES THAT GET IT HOW MANY

Circle , ,
the big lime cube the small blue cube the small green cube 3 cubes

Tick , ,
the yellow cone the green cone the pink cone 3 cones

Cross , ,
the white cylinder the light blue cylinder the orange cylinder 3 cylinders

Box , ,
the tall pink cuboid the flat pink cuboid the purple cuboid 3 cuboids

The round yellow shape is a sp r he e. It gets no mark.

− Exp anat on
l i

Why A : cube has all six faces of the same size. A cuboid has flat faces too, but
some f ces a are longer than others.

Page 18 of 45

as e
l h h e

a g l A aS m · NCERT So ut ons
gl e l i

Na e he ha e : co m
m.
Q2
e
m t s p s

m
• with no edges.
l as
m .co a g
l a se
a g

co m
em . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
g
aT s ap s pr nt
he h e i n the book, drawn again.
ed i

co m
m .
as e
Rm
A NSWcE o g l
.
mre. A sphere has no edges. a
Sspehe
a
agl ball is a sphere. Run your finger over it. You never feel an edge or a corner.
m
A

m l a se
Why A cfoace g
m. a
a
n edge is m de where two s meet. A sphere has only one face, so no
ase
:

agl
a
two f ces c n meet. a

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co

a g l Page 19 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q3 Na e he ha e :
m t s p s

• i h l fla face .
wt on y t s

T
he shapes printed in the book, drawn again.

Cu an
be d c uo b id.

Each has 6 faces, and all of them are flat.

− Exp anat on
l i

Why A a a : fl t f ce touches the table everywhere, so the shape does not roll away.

Did you know? Your book says a cube is a special kind of cuboid All its . 6 f aces
are of the same size.

Page 20 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q4 Na e he ha e :
m t s p s

a
• with only curved f ces.

T
he shapes printed in the book, drawn again.

Sphere.
A ball, a marble and an orange are spheres. Their whole outside is one curved face.

Why A : a a a
sphere h s no fl t p rt to sit on. That is why it rolls in every direction.

Page 21 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q5 Na e he ha e :
m t s p s

• i h b h aigh a d c
wt ot str t n urved edges.

T
he shapes printed in the book, drawn again.

Cy n
li de r an on d c e.

The round rim at the bottom is a curved edge.
The line down the side looks straight.

− Exp anat on
l i

Tip: A cube and a cuboid have only straight edges. A sphere has no edge at all.

Why B : oth sh pes a are round at one end and straight along the side, so you see
two kinds of lines on them.

Page 22 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q6 Na e he ha e :
m t s p s

• i h b h fla a d c
wt ot t n ed f ces.
urv a

T he shapes printed in the book, drawn again.

Cy n
li de r an on d c e.

Cylinder → 2 flat round faces + 1 curved face

Cone → 1 flat round face + 1 curved face

− Exp anat on
l i

Why S a : a cylinder up and it does not move, because a flat face is on the
t nd

table. Lay it down and it rolls, because now the curved face touches the table.

Let us Do — Page 13

Page 23 of 45

as e
l h h e

a g l A aS m · NCERT So ut ons
gl e l i

Questions 4 and 5  building shapes
co m
e m.
Which.cohm
a e ca g l as
a
Q1 build?
m
s p s n you

l a se
ag

co m
em . ag
g l as
a

co m
e m.
m l as
m .co a g
l a se
a g
m a s
T .co
two frames made with clay balls and sticks.
m agl
se
he

g l a
a
m
Sample answer: I can build shapes with only straight edges, like a cube or .aco
cuboid.

se m
cofm g l a
.
irst rame clay balls and sticks
a
sem
F :4 6 .

Second frame a u
a
or cuboid with clay balls and icks.
agl
: c be ( ) 8 12 st

− Exp anat onl i

se m
o m g l a
m .cr one way call it a cuboid oth answers are right
f the second frame looks a little longe
a
Sticks of two lengths make a cusbeoid
I , .B .

You cannot build a ball aacg
la
.

ylinder or a cone this way Their faces are curved and a stick is
, . ,

stra ight.

. com
Wmhy Ea e a edge a d each cla ball bec em
a s e ac

co agl
: ch stick becom s n n y om s orner.

m .
ase
a g l
.c
s e m
m a
e m . co agl
g l as
a

com
m .
m as e
.co

a g l Page 24 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q2 T ry to m ake he e ha e
t s s p s us n i g cubes.

T he two shapes the book asks you to make with cubes.

F rst s ap : 8 u
i h e c bes You can see One cube is hidden at the corner under the tall part
. 7. , .

Second shape: 5 c be . u s Stand cubes one above the other Join cube in front of the middle
3 . 1

cube and 1 behind it.

− Exp anat onl i

Build the first shape step by step:
 Put 1 cube at the corner.
 Add 2 cubes going to one side.
 Add 3 cubes coming towards you.
 Add 2 cubes going straight up.

1 + 2 + 3 + 2 = 8 cubes

3 + 1 + 1 = 5 cubes

Seen from the side, the second shape looks like a plus sign.

Why Ea : ch cube has flat faces. Two flat faces fit together neatly, so the shape

a
st nds up.

Page 25 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Let us Play — Page 12–13
s
Added practice: the board game along the border

Q1 a a a a a a
he bo rd g me long the border of p ges 12 nd 13, e ch number on the die st nds
In t a
a a
for sh pe: 1  cylinder, 2  sphere, 3  cone, 4  cube, 5  cuboid, 6  move 2
a S a
steps forw rd. ort these border pictures by sh pe: globe, book, ice-cream cone,

drum, ball of wool, die, chalk, eraser, orange, carrot, bottle, party cap, gift box,
football.

SHAPE ( DIE NUMBER) PICTURES

Cylinder 1 drum, chalk, bottle

Sphere 2 globe, ball of wool, orange, football

Cone 3 ice-cream cone, carrot, party cap

Cube 4 die, gift box

Cuboid 5 book, eraser

f you roll a 3, move your counter to the next cone picture.
I

Let us Do — Page 14

Page 26 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Questions 6, 7 and 8

Q1 In w a a a a a a a a
h t w ys re these sh pes the s me? In wh t w ys re they different?

T
he fi ve shapes printed in the book.

Same: all five are solid shapes. Each one takes up space.
Diffe er nt their faces are different and only some of them roll
: , .

SHAPE FLAT FACES CURVED FACES DOES IT ROLL?

Cylinder 2 1 ,
yes when lying down

Cube 6 0 no

Cone 1 1 ,
yes round and round

Cuboid 6 0 no

Sphere 0 1 ,
yes every way

− Exp anat on
l i

You can hold each one in your hand, and each one can be made from clay.

Page 27 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Why A a a: fl t f ce stops a shape from rolling. So shapes with only flat faces stay

where you put them.

Q2 L k a a die. The face ha e 1
oo t s v to 6 dots. Wha t num a
ber is on the f ce opposite number
1?

A die. On y t r
l h ee f a s can be seen at a time.
ce

The face opposite 1 has 6 dots.

1+6=7

Page 28 of 45

as e
l h h e

a g l A aS m · NCERT So ut ons
gl e l i

co m
m.
− Exp anat on
l i

m as e
.co
Take a die in your hand. Keep the 1 on top and turn it over. You will see 6 at the bottom.
a g l
a s em
aglWhy O a die : n , two opposite f aces always add up to 7.

co m
m . ag
l a se
Q3 Wha t num ber is on t he faceag ie
oppos t num ber 2?

co m
em.
m l as
m .co a g
l a se
a g
m a s
m.co agl
l a se
a g

com
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl

co m
m .
m l a se
m .co s ag
ase
A die. On y t r
l h ee f a s can be ee
ce n at a t m
i e.

agl c
m .
m a s e
co agl
The face opposite has dots m.
a se
2 .

l
5

ag

co m
m .
m ase
.co

a g l Page 29 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

2+5=7

− Exp anat on
l i

Keep the 2 in front of you. The face hidden at the back is the 5.

Why T : a
wo opposite f ces of a die always add up to 7. To find the partner of 2,
a
t ke 2 away from 7 7  2  5.

Page 30 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q4 Wha t num a
ber is on the f ce opposite number 3?

A die. On y t r
l a
h ee f s can be seen at a time.
ce

The face opposite 3 has 4 dots.

3+4=7

So the three pairs on a die are 1 and 6, 2 and 5, 3 and 4.

Page 31 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q5 Wha a e d
t p tt rn ice?
o you not

A die. On y t r
l a
h ee f s can be seen at a time.
ce

The numbers on opposite faces always add up to 7.

1+6=7

2+5=7

3+4=7

One number goes up by 1 and the other goes down by 1.

− Exp anat on
l i

A die has 6 faces. They make 3 pairs of opposite faces, and every pair adds up to 7.

Page 32 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Check it yourself: Look at any die at home Add the top number and the bottom
.

number. You will get 7 every time.

Q6 In w a
h t order is this model built?

The model built from planks, pillars, cones and small blocks.

 Keep 2 cuboid blocks on the ground.
 Lay a flat cuboid plank on them.
 Stand 4 cylinders on the plank.
 Put another cuboid plank on the cylinders.
 Put 4 cones on the top plank.
The 3 sma u o s under the middle make steps from big to small
ll c b id , .

− Exp anat on
l i

The model is built from the bottom upwards. The two blocks go one at each end. The small
steps can be put there first or last.

Page 33 of 45

as e
l h h e

a g l A aS m · NCERT So ut ons
gl e l i

Why A co m
m.
: I
block cannot be put in the air. t needs something under it to hold it.

m as e
.co a g l
a s em
agl
Let us Do — Page 15
co m
Questions 9, 10 and 11, and the childrenʼs questions
m . ag
l a se
Q1 Wha ha e d
ts p o you ge if agj i a c be a d a c b id?
t you o n u n u o

co m
e m.
m l as
m.co a g
l a se
a g
m a s
m .co agl
l a se
ag

co m
m .
m as e
.co
A u an a u o
g l
ying on the table.
a
m
c be d c b id l

l a se
ag
se m
com g l a
You get a bigger cuboid.
m . a
ase
agl

co m
m .
m ase
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m as e
.co

a g l Page 34 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

T he same two shapes pushed together.

Join the cube to the end face of the cuboid. The new shape has 6 flat faces, so it is a cuboid.

− Exp anat on
l i

This works when the two faces that touch are of the same size. If they are not, the new
shape has a step and is not a cuboid.

Why Y : our book s ys a a cube is a special kind of cuboid. Joining two cuboids
face to face gives one longer cuboid.

Q2 How m a
ny a a
cubes re used to m ke this sh pe? a

T r s stack of small coloured cubes on a round table, drawn simply.
he gi lʼ

u s
21 c be . Count layer by layer.

Page 35 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Top layer: 5

Middle layer: 7

Bottom layer: 9
5 + 7 + 9 = 21

You can see 14 cubes. 7 more are hidden under them.

− Exp anat on
l i

Every cube you see on top needs cubes under it to hold it up, so the hidden places must
be filled. The bottom layer is 3 rows of 3 cubes: 3  3  3  9.
Bu ild the same stack with your own cubes and count them to check.

Q3 In a a a T a
how m ny different w ys c n you join 3 cubes? ry nd see.

Tr
h ee c ubes joined in a line.

In 2 diffe e r nt ways .

Page 36 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

1 2

The two shapes you can make with three cubes.

 All three in a straight line — a long cuboid.
 Two in a line and the third at the side — an L shape.

− Exp anat on
l i

Why J : oin two cubes first. The third cube can go either at the end of the line or
at a side. There is no third choice.

Page 37 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q4 Wha t poss a
ible sh pes do you get if you join 3 cubes?

Trh ee c ubes joined in a line.

Two shapes: a long cuboid 3 cubes in a line) and an L shape.

1 2

T
he two shapes you can make with three cubes.

Page 38 of 45

as e
l h h e

a g l A aS m · NCERT So ut ons
gl e l i

co m
m.
− Exp anat on
l i

m as e
.co
Turn the L shape around and it is still an L. So it is not a new shape.
a g l
a s em
aglWhy T : urning a shape does not change it. Only a new place for a cube makes a
new sh pe. a

co m
em . ag
g l as
a
Q5 Na e he ha e ed in these models. Describe how the sh pes re rr nged. a a aa
m
m t s p s us

co
e m.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
ag
(a) b
( ) c
( ) d
( )

co m
T our models (a), (b), (c) and (d) from the book.
m .
e
he f

m l as
m .co a g
a s eNSW
agl A our mo s us on y u o s
A ER

se m
ll f del e l c b id .

omit (one out on each side), a small yellow between
c g l a
.
 (a) Orange at the bottom, two green on
e m a
agsreen one on top — like a T.
hem, red on top.
l
t

 (b) 5 in a column with a wgide
a
 (c) 6 stacked, red and orange by turns — a tower.
 (d) 3 stacked, each pushed a little to one side — like steps.
co m
m .
− oEm as e
.c
xp anat on
a g l
m
l i

ase The blocks are of different sizes and colours but every block has flat faces so each one
agl
, 6 ,

.c
is a cuboid.

s e m
m a
Why F a a . co
l t f ces rest on flat faces, so cuboids stack well. n (d) the blocks are
m
I
agl
se
:

shifted, so the st ck looks like a
g l a a staircase.
a

co m
m .
m ase
.co

a g l Page 39 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Q6 U e i dice
s sx to m ake he f ll
t o ow n a aa
i g sh pes: ( ) cuboid (b) a a
e c) ny other sh pe
tow r ( a
f
o your choice

Sx
i dice. Ea s a cube.
ch die i

a A cuboid  3 dice in a row, and 3 more on top.
( )

Sx
i dice: three in a row with three more on top.

(b) A tow r  6 dice one on another.
e

Page 40 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Page 41 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Page 42 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Sx
i dice put one on another.

(c) Sample answer: steps  3 in a row, 2 on them, 1 on top.

Sx i dice made into steps.

Page 43 of 45

as e
l h h e

a g l A aS m · NCERT So ut ons
gl e l i

co m
em.
3 + 2 + 1 = 6 dice
m l as
.co a g
− Expsaenm
a
agl
at on
l i

Every die is a cube, so six dice can be put together in many ways.

Why A a a cuboid too — m
om
.c a thin, tall one. Six cubes can make ag
e
l f scubes stays 6.
: t ll tower is just

many shapes, but the number oa
ag

co m
e m.
m l as
.co a g
a s em
agCl hapter at a glance
ery solid shape has faces, edges and corners. A face is a side, an edge is where two
meet. a s
agl
Ev

faces meet, and a corner is where edgecsom
.
me size. A cuboid has 6 flat faces too. The book says a
A cube has 6 flat faces, all of the se
a s
bogidl .
am
cube is a special kind of cua
A cylinder has 2 flat round faces and 1 curved face. A cone has 1 flat round face, 1 curved

face and a pointed tip.
. c om
s em
A sphere is a ball. It has only one curved face, no edge and no corner, so it rolls every way.

m a
.
Toyscoand models are made by joining shapes. Say what is onatop gl of what, and what is
a s emunder what, to describe a model.
agl On a die the faces show 1 to 6 dots. The dots on two opposite faces always add up to 7.
se m
com g l a
m . a
ase
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

com
m .
m ase
.co

a g l Page 44 of 45

l h h e A aS m · NCERT So ut ons
gl e l i

Quick revision

SHAPE FLAT FACES CURVED FACES SOMETHING THAT LOOKS
LIKE IT

Cube 6, all of the same size none A die

Cuboid 6 none A duster or a book

Cylinder 2 round faces 1 A water bottle

Cone 1 round face 1 A birthday cap

Sphere none 1 A ball

Edges Cube and cuboid have Cylinder and cone have round A sphere has no edge
straight edges edges

Corners A cube has 8 corners A cuboid has 8 corners A cone has one pointed tip

Rolling Cube and cuboid do not roll Cylinder, cone and sphere roll A flat face stops a roll

A die 6 faces, 1 to 6 dots Opposite faces add up to 7 1 with 6, 2 with 5, 3 with 4

Page 45 of 45