volume by counting cubes objective to understand the concept of volume in terms of counting cubes

VOLUME BY COUNTING VOLUME BY COUNTING CUBESCUBES

ObjectiveObjective

To understand the concept of volume in terms of counting

cubes.

WHAT IS VOLUME?WHAT IS VOLUME?

Volume is the measure of the capacity of a container.

It is the measure of how much a container of a particular shape will hold - liquids, dry substances, etc.

= 1 centimetre cube

1cm 1cm

1cm

= 1 cm³

One Unit of Volume is the “CUBIC One Unit of Volume is the “CUBIC CENTIMETRE”CENTIMETRE”

Volume is the amount of space a 3D - shape takes upVolume is the amount of space a 3D - shape takes up

Volumes by Counting Volumes by Counting CubesCubes

= 2 centimetre cubes

1cm

1cm

1cm

= 2 cm³

This shape is made up of 1 centimetre cubes placed next to each other. What is its volume

in cm³?

1cm

Volumes by Counting Volumes by Counting CubesCubes

What is its volume in cm³ of these shapes.

5 cm3

6 cm3

5 cm3

Volumes by Counting Volumes by Counting CubesCubes

Volume = 24 centimetre cube

One unit of Volume is the “CUBIC One unit of Volume is the “CUBIC CENTIMETRE”CENTIMETRE”

2cm

3cm

4cm

= 24 cm³

Volumes by Counting Volumes by Counting CubesCubes

Volumes by Counting CubesVolumes by Counting Cubes

a. ____ cm³

b. ____ mm³

A. 32 A. 32 CMCM ³³B. 15CM³B. 15CM³

c. ____ cm3 d. ___ cm

3

A. 27 CM A. 27 CM ³³B. 12CM³B. 12CM³

Now try theseExercises!

Volume in term of Volume in term of cubescubes

ANSWERSANSWERS

VOLUME OF CUBES AND VOLUME OF CUBES AND CUBOIDSCUBOIDS

OBJECTIVE: To understand how to calculate the

volume of cuboids and cubes.

How can we find VOLUME of a cube?

CUBESCUBES

a

All the sides (edges) of a cube have the same

length. If each side has the length  a, the

formula for the volume V will be: 

L x L x L

x

a

Example 1

2cm

Volume = l x l x l

V = 2 x 2 x 2

V = 8 cm³

Working

34cm

34cm

34cm

Example 2Working

Volume = l x l x l

V = 34 x 34 x 34

V = 393cm3

Volume of a cuboid

4 layers of 18 cubes= 4 x 18

= 72 centimetre cubes = 72 cm³

18 cubes fit the base.

= 1 centimetre cube = 1 cm³

3cm

4cm

6cm

A short cut !

6 = 72 cm³ Volume =

length

x Breadth

x 4 x height

length

breadth

height

x 3 Volume =

3cm

4cm

6cm

Volume = l x b x h

V = 18 x 5 x 27

V = 2430 cm³

Example 1

18 cm5 cm

27cm

Heilander’sPorridge Oats

Working

2 cm

3 mm3 mm

4 mm

7 cm6 cm

9 ft

4 ft6 ft

Volume of Cuboids

Volume = 4 mm x 3 mm x 3 mm = 36 mm3

Volume = 2 cm x 7 cm x 6 cm = 84 cm3

36 mm3

36 mm3

84 cm384 cm3

Volume = 9 ft x 4 ft x 6 ft = 216 ft3

216 ft3

216 ft3

Volume l x w x h

? yards3

Now try theseExercises!

Volume of Volume of cuboids and cuboids and

cubescubes

VOLUME OF CYLINDERSVOLUME OF CYLINDERS

4cm

6cm

It has a height of 6cm .

What is the size of the radius ?

Volume = cross section x height

Calculate the area of the circle:

A = r 2

A = 3.14 x 2 x 2

A = 12.56 cm2

Calculate the volume:

V = r 2 x h

V = 12.56 x 6

V = 75.36 cm3

The formula for the volume of a cylinder is:

V = r 2 h

r = radius h = height.

2cm

VOLUME OF VOLUME OF CYLINDERSCYLINDERS

Radius is the half of diameter

The formula for the volume of a cylinder is:

V = r 2 h

r = radius h = height.