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6.025 Scale ratios

Worksheet
Scale ratios
1

Express the following scales as simplified ratios:

a

1 \text{ cm} represents 240 \text{ cm}.

b

1 \text{ cm} represents 2 \text{ km}.

c

3 \text{ cm} represents an actual distance of 9 \text{ m}.

d

5 \text{ cm} represents an actual distance of 30 \text{ km}.

e

60 \text{ mm} represents an actual distance of 5400 \text{ m}.

f

98 \text{ mm} represents an actual distance of 9.8 \text{ km}.

2

A map has been drawn to a scale of 1:7000.

a

Find, in millimetres, the actual distance between two points which are drawn 8 \text{ mm} apart on that map.

b

Find the distance in metres between the two points from part (a).

3

On a house plan that has been drawn to a scale of 1:100, the building is drawn to a length of 158 \text{ mm}.

a

Find, in millimetres, the actual length of the building.

b

Find the actual length of the building in metres.

4

A commercial plane measuring 66 \text{ m} long is to be represented on a scale model with a scale of 1:100. Find, in metres, the length of the plane in the scale model.

5

The scale on a map of a garden is 1:2000. The actual distance between the fountains is 100 \text{ m}.

a

Find the actual distance between the two fountains in centimetres.

b

Find the distance in centimetres between the two fountains as points on the map.

6

Bianca is looking over a map of her local area and notices that the scale of the map is given as 1:100 in the map legend.

a

Find, in centimetres, the actual distance between two points which are drawn 12 \text{ cm} apart on that map.

b

Find the distance in metres between the two points from part (a).

7

Given that the scale on a map is 1:25\,000, find the actual distance between two points which are drawn 14 \text{ cm} apart on the map in the following units:

a

Centimetres

b

Kilometres

8

The scale on a map is 1:400\,000. How far apart on the map should two train stations be drawn if the actual distance between the stations is 100 \text{ km}? Express your answer in centimetres.

9

Consider the elephant picture which is next to a centimetre ruler. The scale of the picture to a real elephant is 1:100.

Find the height of the real elephant in metres.

10

Consider the picture of a goldfish next to a centimetre ruler. The scale of the picture to a real goldfish is 2:1.

Find the length of the real goldfish.

11

For the house floor plan below:

a

Use the scale to find the width (horizontal) and length (vertical) of the kitchen.

b

Calculate the total floor area of the house.

12

Consider the given floor plan:

a

According to the scale of the diagram, 1 \text{ cm} on the diagram represents how many metres in the house?

b

Using a ruler, Neville measures the length of Bed 1 on the plan and finds it to be 4 \text{ cm}. How many metres does this represent?

c

Using a ruler, Neville measures the width of Bed 1 on the plan and finds it to be 8 \text{ cm}. How many metres does this represent?

d

Neville wants to tile the floor of Bed 1. If each tile is 20 \text{ cm} by 10 \text{ cm}, how many tiles would Neville need?

e

If each tile weighs 200 \text{ g}, calculate the total weight of the tiles in grams.

f

Due to building regulations the total weight of the tiles cannot be more than 325 \text{ kg}. Convert your answer from part (e) to kilograms and determine if Neville will be able to use these tiles on the floor.

13

Koala airlines has a simplified scale map of Australia which shows the cities it flies between. The the distance flown from Adelaide to Brisbane is 1600 \text{ km}.

Estimate the real distance the scale bar represents to the nearest 100 \text{ km}.

14

The following is a 1:58\,000 scale drawing of the sailing route from the mainland to an island off the coast. The captain approximates the distance to be 15.3 \text{ cm} on the map.

Estimate the distance in kilometres of the boat trip.

15

Jimmy has a globe of the world that spins around so he can see where all of the countries that he wants to travel to are. The globe has a scale such that 1\text{ cm} on the globe represents a distance of 1000\text{ km} in real life.

State the scale ratio for this globe.

16

A swimming pool of length 40\text{ m} and width 20\text{ m} is to be represented on a scale drawing with a scale of 1:2000. Find the scale dimensions of the pool in centimetres.

a

Find the length in centimetres.

b

Find the width in centimetres.

17

Nadia has just arrived in Bali for her holiday and is trying to work out how far apart certain places are to decide if she can walk between them or if she needs to catch a taxi.

She has checked-in to the Villa Nagal and wants to get a drink at De ja vu. According to the map, what is the closest real-life distance between De ja vu and Villa Nagal?

A

200\text{ m}

B

600\text{ m}

C

800\text{ m}

D

400\text{ m}

18

The following is a 1:200 floor plan of a house. The homeowner wishes to add a dining room table, which is 250\text{ cm} long and placed where the \times is marked on the floor plan:

What length should the table be drawn on the floor plan?

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Outcomes

1.2.3.2

use the scale factor for two similar figures to solve linear scaling problems

1.2.3.3

obtain measurements from scale drawings, such as maps or building plans, to solve problems

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