SUBJECT: MATHEMATICS
CLASS: JSS 3
DATE:
TERM: 2nd TERM
WEEK TEN DATE---------------
TOPIC: SCALE DRAWING
Using Scales
A scale is a ratio or proportion that shows the relationship between a length or a drawing and the corresponding length on the actual object.
Thus,
Scale = Any length on scale drawing
Corresponding length on actual object
Worked Examples
actual length of the billboard if the scale is 1cm represents 2m?
Solution
1cm represents 2m
5cm represents 5 × 2m = 10m
The actual length of the billboard = 10m.
length on the drawing.
Solution
500m is represented by 1cm
1m is represented by 1/500cm
6000m is represented by 6000 × 1/500 = 12cm
Length on drawing = 12cm
Evaluation:
Actual length | Scale | Length on drawing |
20m | 1cm to 5m | |
450m | 1cm to 100m | |
65m | 1cm to 5m |
Length on drawing | Scale | Actual length |
11cm | 1cm to 5m | |
8.2cm | 1cm to 100m | |
12.6cm | 2cm to 1m |
Scale Drawing
Scale drawing is very important to engineers, architects, surveyors and navigators. For an accurate scale drawing, mathematical instruments are needed such as pencils, a ruler and a set-square. Also, the dimensions of the actual objects are written on the drawing.
Worked Examples
Solution
Firstly, make a rough sketch of the plan
45m
30m
Secondly, choose a suitable scale
Using 1cm represent5m will give a 9cm by 6cm rectangle.
The distance between the opposite corners of the field is represented by the dotted line. Length of the dotted line = 10.75
Actual distance = 10.75 × 5 = 53.75m = 54m (to the nearest metre)
Example 2:
Points A and B are 178m and 124m from X respectively. The distance between A and B is 108m. Make a scale drawing of the path and find the angle between the paths and X. X
Solution 178m 124m
A B
108m
Using a suitable scale of 1cm to 20m, the sides of the triangle in scale drawing will be as follows:
AX = 178/20 = 8.9cm, BX = 124/20 = 6.2cm, AB = 108/20 = 5.4cm.
X
178m 124m
A 108m B
Using a protractor, AXB = 370 (to the nearest degree). The angle between the paths is 370.
Evaluation:
Application of Scale Drawing on Related Problems
Worked Examples
Solution
Note: Map scale = actual distance/distance on the map.
∴ Distance on map = Actual distance / Map Scale
5.5cm represent 50,000 × 5.5 = 275,000cm
To correct to km = 275,000/100,000 = 2.75km.
4km = 100,000 × 4 = 400,000cm.
Since 50,000cm represents 1cm
400,000cm is represented by 400,000/50,000 = 8cm
or Distance on the map = Actual distance / Map Scale
= 400,000 / 50,000 = 8cm.
Example 2:
Two cities are 70km apart. The distance between them is 20cm on the map. What is the scale of the map?
Solution
1km = 100,000cm
∴ 70km = 100,000 × 70 = 7,000,000cm
Map scale = actual distance/distance on map.
= 7,000,000/20 = 350,000
The scale of the map = 1 : 350,000.
Evaluation: Class Work
by a) 5cm b) 10cm
READING ASSIGNMENT:
NGM Bk 2 Chapter 16, Pages 133 – 134.
Essential Mathematics for JSS Bk 2, Chapter 17, Pg 166 – 169
WEEKEND ASSIGNMENT
polygon has. a) 11 b) 21 c) 16 d) 13
QR = 3cm and TQ = 4cm, what is PS?
rhombus? a) 8cm b) 7cm c) 10cm d) 5cm
THEORY
1.The scale on the map is 2cm : 30,000km
Find the distance in km between two islands represented by a distance of 20cm on the
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