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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
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