Maths Quest A Year 11 for Queensland
WorkSHEET 7.1
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Chapter 7 Basics of construction WorkSHEET 7.1
Basics of construction
Change the following scales into ratio form.
(a) 1 cm represents 100 km
(b) 1 cm represents 250 km
(c) 1 cm = 425 m
(d) 1 cm = 19 km
Name: ___________________________
(a) 100 km = 100  1000 = 100 000 m
100 000 m = 100 000  100
= 10 000 000 cm
1: 10 000 000
(b) 250 km = 250  1000 = 250 000 m
250 000 m = 250 000  100
= 25 000 000 cm
1: 25 000 000
(c) 425 m = 425  100 = 42 500 cm
1: 42 500
(d) 19 km = 19  1000 = 19 000 m
19 000  100 = 1 900 000 cm
1: 1 900 000
2
Find the distance represented by 1 cm on a map
if the scale was written as:
(a) 100 cm = 100  100 = 1 m
1 cm represents 1 m
(a) 1: 100
(b) 1400 cm = 1400  100 = 14 m
(b) 1: 1400
1 cm represents 14 m
(c) 1: 70 000
(d) 1: 8 000 000.
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A map is drawn to the scale 1 cm = 40 km.
Find the distance on the map for the following
actual distances.
(c) 70 000 cm = 70 000  100 = 700 m
1 cm represents 700 m
(d) 8 000 000 = 8 000 000  100 = 80 000 m
80 000 m = 80 000  1000 = 80 km
1 cm represents 80 km
(a)
120  40 = 3 cm
3 cm represents 120 km
(b)
400  40 = 10 cm
10 cm represents 400 km
(c)
2000  40 = 50 cm
50 cm represents 2000 km
(d)
660  40 = 16.5 cm
16.5 cm represents 660 km
(a) 120 km
(b) 400 km
(c) 2000 km
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(d) 660 km
Maths Quest A Year 11 for Queensland
4
Chapter 7 Basics of construction WorkSHEET 7.1
A map is drawn to the scale of 1: 50 000. Find
the actual distance represented by a
measurement on the map of:
50 000 cm = 50 000  100 = 500 m
(a)
4  500 = 2000 m
2000 m  1000 = 2 km
(b)
18  500 = 9000 m
9000 m  1000 = 9 km
(c)
62  500 = 31 000 m
31 000 m  1000 = 31 km
(a) 4 cm
(b) 18 cm
(c) 62 cm.
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The figure above is a map of Victoria. Using the scale given, measure and then calculate the
actual distance from:
1 cm represents 50 km
(a) Bendigo to Melbourne
(b) Ouyen to Bright
(a) 3 cm = 3  50 = 150 km
(c) Hamilton to Wangaratta
(b) 10.5 cm = 10.5  50 = 525 km
(d) Corryong to Lakes Entrance
(c) 9.5 cm = 9.5  50 = 475 km
(d) 4 cm = 4  50 = 200 km
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Maths Quest A Year 11 for Queensland
6
Chapter 7 Basics of construction WorkSHEET 7.1
Redraw this floor plan using a scale 1 : 200.
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Maths Quest A Year 11 for Queensland
7
Chapter 7 Basics of construction WorkSHEET 7.1
Give the actual dimensions of the three
bedrooms in the house plan in question 6.
The scale is 1 : 100 so the actual measurements
are 100 times those measured on the map.
Bedroom 1
Map measurements: 3.8 cm by 3.8 cm
Actual measurements:
(3.8 cm  100) by (3.8 cm  100)
= 3800 cm by 3800 cm
= 3.8 m by 3.8 m
Bedroom 2
Map measurements: 3.8 cm by 2.9 cm
Actual measurements: 3.8 m by 2.9 m
Bedroom 3
Map measurements: 3 cm by 2.8 cm
Actual measurements: 3 m by 2.8 m
8
The diagram below represent the front
elevation of a house
Reproduce this plan using a scale of 1 : 100.
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Maths Quest A Year 11 for Queensland
9
Chapter 7 Basics of construction WorkSHEET 7.1
Using the front elevation in question 8,
determine the actual height of the peak of the
roof above the floor level.
Scale is 1 : 200.
This means that the actual measurements are
200 times the plan measurements.
Plan measurement from peak of roof to floor
level = 3.4 cm.
Actual measurement
= 3.4 cm x 200
= 680 cm
= 6.8 m
So, the peak of the roof is 6.8 m above the floor
level.
10
Determine the actual size of the door in the
front elevation shown in question 8.
Scale is 1 : 200.
Measured width of door = 0.7 cm.
So, actual width of door
= 0.7 cm x 200
= 140 cm
= 1.4 m
Measure height of door
= 0.9 cm
So, actual height of door
= 0.9 cm  200
=180 cm
= 1.8 m
So, the door is 1.8 m high and 1.4 m wide.
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