Express each of the following as a scale ratio in the form 1:k if 1\text{ cm} represents an actual length of:
Express as a ratio the scale on a map if a map distance of:
2\text{ cm} represents an actual distance of 20\text{ m}
40\text{ cm} represents an actual distance of 5\text{ km}
15\text{ mm} represents an actual distance of 30\text{ m}
On a map, 7 \text{ cm} represents a distance of 63 \text{ km}.
Fill in the box to complete the simplified ratio 1:⬚.
Find the actual distance (in kilometres) represented on the map by 5 \text{ cm}.
Find the map distance (in centimetres) that represents an actual distance of 54 \text{ km}.
A map has been drawn to a scale of 1:1000. Find, in metres, the actual distance between two points A and B if the distance AB on the map is:
A map has been drawn to a scale of 1:20\,000. Find, in metres, the actual distance between two points A and B if the distance AB on the map is:
A map is to be drawn to a scale of 1:20\,000. How far apart on the map should two points be drawn if the actual distance between the points is:
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.
Find the actual distance in centimetres between two points which are drawn 12 \text{ cm} apart on the map.
Hence find the actual distance in metres between the two points.
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}. Find the actual length of the building in metres.
A commercial plane measuring 66 metres 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. Give your answer in metres, correct to two decimal places.
The scale of the map is 1:2000 and two points are drawn 19 \text{ cm} apart on the map.
Find the actual distance between the two points in centimetres.
Find the distance between the points in metres.
The scale on a map of a garden is 1:2000. How far apart on the map should two fountains be drawn if the actual distance between the fountains is 100 metres? Express your answer in centimetres.
Find the distance between two lakes drawn on a map if the scale on the map is \\1\text{ cm} : 3 \text{ km}, and the actual distance between the lakes is 147\text{ km}.
The walk from the roller coaster to the water slide is known to be 450 \text{ m}. The distance on the map between these two rides is 15 \text{ cm}. What ratio is the map using?
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.
Consider a map with a scale of 1:25\,000.
Find the actual distance between two points which are drawn 14 \text{ cm} apart on the map.
Find the distance between the points in kilometres.
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.
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 15.4\text{ cm} on the map. What is the distance in kilometres of the route?
At a fun park, the walk from the roller coaster to the water slide is 240\text{ m}. The distance on the map between these two rides is 12\text{ cm}. What ratio is the map using?
A scale model for a new skyscraper has been constructed and has windows that are 3.87 \text{ cm} wide. The actual windows will be 13.5 \text{ cm} wide. What ratio is the model using?
A school plans a 500\text{ m} race for students. What distance (in centimetres) does this represent on a map with a scale of 1:1000?
The owners of a treetop adventure park wish to connect two trees with a rope. On a map, the length between the two trees on a 1:300 map is 3\text{ cm}. Find the actual length between the two trees.
A map of a town is drawn to scale.
Find the distance between house A and the park.
Find the distance between house C and the park.
Find the length of the shorter side of the park.
Find the length of the longer sider of the park.
Find the distance between house A and house C, in metres, by travelling along the road.
Hence find this distance in kilometres.
Koala airline has a simplified scale map of cities it flies between. Find the distance of the direct route between Sydney and Brisbane.
Koala airline has a simplified scale map of cities it flies between. The distance flown from Adelaide to Brisbane is 1600 \text{ km}. What distance does the scale bar represent?
The following picture represents the difference in width of human and Merino hair.
What is the true width of the Merino hair?
The following picture is a scale drawing of a Tardigrade, a microscopic creature. Emily wants to create a large model of the Tardigrade by enlarging the lengths by a factor of 12.5.
What is the simplified ratio comparing the real size to the model size of the creature?
State what the following abbreviations on a floor plan stand for:
KIT
WC
LIN
SHR
CAB
CBD
O
R
State the abbreviation for the following objects on a floor plan:
Door
Sliding door
Television
Window
Consider the given floor plan:
According to the scale of the diagram, 1 \text{ cm} on the diagram represents how many metres in the house?
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?
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?
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?
If each tile weighs 200 \text{ g}, calculate the total weight of the tiles in grams.
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.
The floor plans of a house are shown in millimetres.
Which side of the house (Northern, Eastern, Western or Southern) is represented by the elevation plan?
What is the length of A on the elevation plan in metres?
The following is a 1:200 floor plan of a house. The homeowner wishes to add a 150\text{ cm} dining table where the X is marked on the floor plan.
What length should the drawn table be on the floor plan?
The floor plans for a house are shown in centimetres:
Determine which side of the house (Northern, Eastern, Southern, Western) is shown in the elevation view.
Find the width of the eastern side in metres.
Hence state the width of the western side in metres.
The floor plans for a double bedroom and ensuite are given below:
What do these symbols represent on the floor plan?
What is the distance between the sink and the shower?
What is the distance between the toilet and the ensuite door?
The floor plans for a two room house are given below with measurments recorded in millimetres:
Which side of the house (Northern, Eastern, Western or Southern) is represented by the elevation plan?
Find the value of A on the elevation in metres.
The floor plans for a double bedroom and ensuite are given below:
What does the following symbol represent on the floor plan?
Find the distance between the shower and the toilet.
Find the distance between the sink and the shower.
Find the distance between the toilet and the ensuite door.
The original plan of a building with ratio 1:100 is enlarged so its length and width are both doubled.
What is the new scale ratio for the plans?
Can the original scale ratio be used for the new enlarged copy of the plan?
The scale bar on the original plan represents 5\text{ m}. When the plan is doubled what length does the scale bar represent?
Can the original scale bar be used for the new enlarged copy of the plan?