M7 Measurement : Volume

VOLUME

         (1) a measure of the space taken up by a solid object.

         (2) It is three-dimensional measurements

<<< All measurements must be in the same units.  >>

LINK BETWEEN AREA AND VOLUME

SQUARE

                                    Area of square = side x side

         

Cube

 (1)  All 6 faces are square

 (2)  All its angles are right angles

 (3)  Volume = side x side x side

RECTANGLE

                             Area A = Length x breadth = L x B

       

Cuboid

(1)  6 rectangular faces                            

(2)  All its angles are right angles                      

(3)  Volume = length x breadth (width) x height                      

VOLUME

                     Volume = Length x Breadth x Height

Volume = Area x Height

DESCRIPTION OF TERMS

VOLUME CALCULATION

Example

Each of the following diagrams represents a shape made from unit cubes.

Unit cube = square of side 1 cm.

               

Example

Find the Volume.

             

Both have the same volume

Volume of one blue cube = 1cm x 1cm x 1cm = 1cm³

No of cube = 8.

Volume of blue cuboid = 1cm³ x 8 = 8 cm³

Volume of red cuboid     = length x breadth x height

                                                 = 4cm x 2cm x 1cm = 8cm³

Example

                 

The above box is a cuboid of length 1 m, width 20 cm and height 30 cm. Work out its volume.

Method

Step 1: Circle/Underline keywords / given values

[Convert to same measurements? 1m = 100cm  (since the other 2 are in cm)

Step 2: Draw and write required formula  V = L x B x H

L = 100cm, B = 20cm, H = 30cm

Step3:  Solve : Use the formula with L, B and H

                Volume = 100 cm x 20cm x 30cm

                              = 60000cm³

Example

Tommy wants to build a patio that will be 2 metres wide,  8 metres long and 10 cm deep. How much concrete will he need?

Method

Step 1: Circle/Underline keywords / given values

[Convert to same measurements? 1m = 100cm  (since the other 2 are in m)

Step 2: Draw and write required formula  V = L x B x H

 (ii) L = 8m, B = 2m, H = 0.1m

Step3:  Solve : Use the formula with L, B and H

             Volume = 8 m x 2m x 0.1m = 1.6m³

CAPACITY AND VOLUME

Capacity is the amount of liquid a solid can contain.

Capacity is usually measured in litres.

1000 cm³ = 1000 millilitres = 1 litre.

       

For example the capacity of:

- a jug

- a teacup or mug

- a food container

- a fish tank

Example

Mary has a rectangular garden pond 2 m long and 1 m wide. She wants to fill it to a depth of
30 cm. How many litres of water will she need?

Method

Step 1: Circle/Underline keywords / given values

            [ Convert measurements? Answer is in litre, then convert to cm]

     2m = 200cm                     1m= 100cm

Step 2: Draw and write required formula  V = L x B x H

 (ii) L = 200cm, B = 100cm, H = 30cm
 

Step3:  Solve : Use the formula with L, B and H

                        Volume = 200 cm x 100cm x 30cm = 600,000cm³

                           1 litre = 1000 cm³
               Bonny needs 600000 / 1000 = 600 litres of water

        ~~~~ END ~~~~ :)