Measurement

AS 1.33 credits

Metric System

Length is measured in metresCapacity is measured in litresWeight in gramsc means one hundredth - 100 cm in 1 metrem means one thousandth – 1000mm in 1 metrek means 1000 - 1000g in 1 kg Convert300 g to kg 30 cm to m2000mm to m 5kg to g300cm to mm 2000mg to kg

0.3kg 0.3 m

2m 5000g

3000mm 0.002kg

PerimeterThe perimeter is the outside edge of a shape.

For a– Polygon, you add the lengths of the sides– Circle , it is 2πr, the circumference

Examples. Find the perimeter of

6cm

3cm 2cm

3cm

2cm

4cm4cm

5cm

5cm

4 cm

Watch all measurements are in the same unit!!!!

6+6+3+3 =18 cm

4+4+5=13 cm

2+2+4+4+3=15 cm

2 π x 5 =31.4 cm

Find the perimeter of

4m

6m

5m

22cm

28m

56cm

36cm

25.2m

100cm

23.1m

15.7m

37.7m

36cm

40cm

17cm

30 mm

24 m

32 mm

35.8 mm

34cm

26 m

32 m

Find the Perimeter

837 m 17.2 m

11.6 km

14.8 cm m4

325 cm

8

325

Circumference of a Circle

dC or rC 2

E.g. Calculate the circumference of these circles

3cm

64mm9.42cm (2dp)

402.12mm (2dp)

Find the perimeter

24cm32cm

20 m40m

h

b

h

b

a

Area• Rectangle

– Area = b x h• Parallelogram

– Area = b x h• Triangle

– Area = ½ b x h

• Trapezium– Area = ½(a + b) x h

• Circle– Area = π r 2

h

b

r 3cm

h

b

4cm

6cm

3cm

8cm

6 cm8cm

A = 4x6 =24cm2

A = 3 x 8 = 24cm2

A = ½6x8 = 24cm2

A = ½(3+6)x2 = ½(9)x2 = ½ x 18 = 9cm2

A = π 32

= 9 π = 28.26cm2

3cm

6cm

2 cm

42.25cm2 54 mm2 30 cm2

35 m2 90 cm2 42 m2

Revision centre

diameter

radius

chord

circumference

arcsegment

sector

56.52 cm

254.34 cm2

37.68 cm

113.04 cm2

Find the area

40cm2

60cm2

12m2

40mm2

5mm

56 cm2 70cm2

117 cm2 187 m2

84.36 mm2

100 mm2

26cm

42cm2

5.6m

1.96m2

503mm

94.2cm

216cm3

12000cm3

Composite Shapes

• To find the area of a compound shape, break it into pieces and find the area of each part

4cm

12cm

248 cm2

200 cm2

48 cm2

144 cm2

80 cm2

244 cm2

1cm

3 cm2

1cm2

4cm2

8cm2

Try these find the light shaded area

13cm2

8cm2

8cm2

8cm2

16cm2

10.2cm2

1.7 m2

6.8 m2

yes

More compound shapes

36

96

52

62.8

53.94cm2

5.46 cm2

Shaded Area

53.94 – 5.46 = 48.48cm2

28 cm2

78cm2Shaded Area = 78 – 28 = 50 cm2

52.5 m2

6.75 m2

200 m

32000 + 59600 = 91600m2

Circles! Find the Area

167.4 m2 4.15 cm2

18.10 m2

227.2 cm28.73 m2

Surface areaTo find the surface area, you find the areas of all the sides of a

shape and add them up• Rectangular Prism

– You have two sides withArea = h x b

– two with sides Area = b x l– two with sides Area = h x l

Surface Area = 2 x (4 x 8) + 2x (8 x 5) + 2 x (4 x 5)= 184m2

b

hl

8m

4m5m

Try these

4m

3m8m

5m

6m10m

12m

5m

4m

10m

5m4m

2 (8x4)+2(3x4)+2(8x3) = 136m2 120+100+60=280 m2

40+120+96 = 256m2

40 + 80 + 100 = 220m2

• Sphere surface area = 4πr2

Surface Area of a Cylinder

25cm

15 cmTo find the surface area of a cylinder we find the area of the circular top and bottom, and then we find the area of the curved surface area.

If we were to flatten it out, it would be a rectangle.

72.1413

450

)15(2 2

Area of circular top

and bottom:

Curved Surface Area:

19.2356

2530

hd

Surface Area: 291.3769

19.235672.1413

cm

301.6cm2

603.2cm2

2789.7cm2318.9cm2

Try these:

Ex 7.7 pg 110

54 cm²

350cm²

396cm²1740cm²

Do Now:A circular stage has an 8m diameter and a height of 30cm. Find the surface area of the stage.

2

2

265.50

4

m

Area of Circle (top)

Area of curved face:

25398.7

3.0)8(

m

Total Surface Area:28.57

5398.7265.50

m

(1dp)

Volume

5m2m

3m

4m5m

3m

4cm

2cm

V = 5 x 2 x 3 = 10 x 3 = 30 m3

V = π x 22 x 4 = 12.57 x 4 = 50.27 cm3

V = ½ x 4 x 3 x 5 = 6 x 5 = 30 m3

Find the volume, given the area of the face

300 m3

315.2 m3

600 m340.6 m3

Find the Volume of these prisms

720 m3324 m3 768 m3

480 m3525 m3

More Volumes…

• Volume of a Pyramid

• Volume of a Cone

• Volume of a Sphere

heightbaseareaV 3

1

hrV 2

3

1

3

3

4rV

These formulas are given to you!

3320

810123

1

cmV

V

3

2

7.1013

8113

1

cmV

V

5m3

3

6.523

53

4

mV

V

Capacity1 cm3 = 1ml

1.How many ml in 10cm3?2.How many ml in 1000mm3?3.How many ml in 1m3?4.How many cm3 in 23ml?5.How many cm3 in 2l?6.How many mm3 in 25ml?7.How many mm3 in 0.5ml?

1. 10 ml2. 1000mm3 = 1cm3

so 1ml3. 1m3=100x100x100

cm3 so 1000000ml4. 23cm3

5. 2l = 2000ml so2000cm3

6. 25ml = 25cm3 so10x10x10x25 =25000mm3

7. = 0.5cm3 =10x10x10x0.5=500mm3

Time

4:106:45

7:25 12:05

7:15 3:50

Time is measured in•Seconds•60 seconds gives a minute•60 minutes gives an hour•24 hours give a day•7 days give a week•52 weeks give a year

Time during the day is measured using 12 hour or 24 hour timeWith 12 hour time am = morning

pm = afternoon12:00 am = midnight12:00 pm = midday

With 24 hour clock, you add 12hours to the pm time. It is always written with 4 digitse.g. 1:30 pm = 12 + 1:30 = 13:00

6:10 am

2:23 pm11:45pm

6:13 am

0:27 am

5:37 pm

8:56 pm

6:28am

9:05pm

4:38am

02:05

17:30

21:15

01:55

12:35

05:2321:45

14:07

11:0718:57

4hours 53 mins

6 hours 22mins

5km

10 mins

2 km

30 mins

4 km 5.5 km/hour

Fearless Flyers

• Build a paper aeroplane (follow the provided instructions if you need them)

• Fly your plane 5 times – each time measuring and recording the distance it flew with a tape measure.

• Use a stopwatch to time the length each flight takes.• Calculate the average of your top 3 values for both

distance and duration. • Using calculate the speed for your

average flight

s

d

t

Distance, speed (velocity) and timeUnits

Distance km or m

Speed km/h or m/s

Time Hours or seconds s

d

t

Distance = speed × time

Speed = distance ÷ time

Time = distance ÷ speed

Try these:1. A car travels for 2 hours at a steady speed of 85

km/h. What distance has it covered?

2. A bus makes a journey of 180km. It takes 3 hours. Calculate the average speed of the bus.

3. A truck travels at an average speed of 75km/h for a distance of 300km. What time does the journey take?

4. How many minutes does it take to run 1500m at an average speed of 10km/h?

170km

60 km/h

4 hours

0.15 hours = 9 minutes

• Rosie, Millie and Hayley are all members of a cycling club. The table shows their training schedule. Complete the missing entries.

1. Change 45km/h into m/s.

2. Change 74m/s into km/h.

3. Change 10.8m/s into km/h.

Distance Speed Time

Rosie 12 km 40 km/hMillie 90 km 2 hoursHayley 60 km/h 1½ hours

18 mins

45 km/h

90 km

12.5 m/s

266.4 km/h

38.88 km/h

$0.87

$46

$6.25

$0.15

12.5cper g if sold per kg13.5c if sold per 100g

Rates

A rate compares two quantities measured in different units. It describes how one quantity changes compared with another.

Speed - compares distance travelled with time taken, often measured in m/s or km/hr.

Growth – compares increase in numbers or size over time.

Eg. A goat eats 110kg of grass in 50 days. Calculate the rate at which the goat is eating per day.110kg = 2.2kg/day 50 complete worksheet 15.01

Do Now:Find the perimeter of this shape: Find the volume

of the golf ball:

3

3

4rV

Find the surface area of the box:

8cm

5cm

3cm

5cm

15cm

61.46cm

r = 1.8cm

24.4cm³

158cm²

Try these:

170 m120 m

240 m

Find the area of this paddock in ha

Work out the volume:a)in cm³b)in litres (round to the nearest whole number)

88cm

52cm

A = 34 800m² = 3.48 ha

a) V = 186 887 cm³

b) 187 litres