Page 143 - Cambridge+Checkpoint+Mathematics+Coursebook+9

15.1 Converting units of area and volume

15.1 Converting units of area and volume

Before you can convert units of area and volume you need to know the conversion factors.
You have already used conversion factors for units of area. Here is a reminder of how to work them out.
!is square has a side length of 1 cm.
!e area of the square is 1 cm × 1 cm = 1 cm . 1 cm = 10 mm
2
!e area of the square is also 10 mm × 10 mm = 100 mm .
2
!is shows that 1 cm = 100 mm . 1 cm = 10 mm
2
2
!is square has a side length of 1 m.
!e area of the square is 1 m × 1 m = 1 m . 1 m = 100 cm
2
!e area of the square is also 100 cm × 100 cm = 10 000 cm .
2
!is shows that 1 m = 10 000 cm .
2
2
1 m = 100 cm
You can use a similar method to work out the conversion factors for volume.
!is cube has a side length of 1 cm.
!e volume of the cube is 1 cm × 1 cm × 1 cm = 1 cm . 1 cm = 10 mm
3
!e volume of the cube is 10 mm × 10 mm × 10 mm = 1000 mm . 1 cm = 10 mm
3
!is shows that 1 cm = 1000 mm . 1 cm = 10 mm
3
3
!is cube has a side length of 1 m.
!e volume of the cube is 1 m × 1 m × 1 m = 1 m .
3
!e volume of the cube is 100 cm × 100 cm × 100 cm = 1 000 000 cm . 1 m = 100 cm
3
!is shows that 1 m = 1 000 000 cm .
3
3
1 m = 100 cm
You already know that 1 litre = 1000 ml. 1 m = 100 cm
You also need to know that 1 cm = 1 ml.
3
!is means that 1 litre = 1000 cm .
3

Worked example 15.1

2
3
3
Convert: a 6 m to cm b 450 mm to cm c 5.3 m to cm d 2300 cm to litres.
3
2
2
2
2
2
2
a 1 m = 10 000 cm Write down the conversion factor for m and cm .
2
6 × 10 000 = 60 000 cm Multiply by 10 000 to convert from m to cm .
2
2
2
2
2
b 1 cm = 100 mm Write down the conversion factor for cm and mm .
2
2
450 ÷ 100 = 4.5 cm Divide by 100 to convert from mm to cm .
2
2
2
3
3
3
3
c 1 m = 1 000 000 cm Write down the conversion factor for m and cm .
3
3
3
5.3 × 1 000 000 = 5 300 000 cm Multiply by 1 000 000 to convert from m to cm .
3
3
d 1 cm = 1 ml Write down the conversion factor for cm and millilitres.
3
2300 cm = 2300 ml Convert from cm to ml.
3
1 litre = 1000 ml Write down the conversion factor for litres and millilitres.
2300 ÷ 1000 = 2.3 litres Divide by 1000 to convert from millilitres to litres.
142 15 Area, perimeter and volume