Scale Drawings

Show your work for each problem.

1.
A map has a scale of . What does this mean?
1. a)1 cm in real life = 10,000 cm on the map
2. b)1 cm on the map = 10,000 cm in real life
3. c)Every 10,000 cm is shown as 10,000 cm
4. d)The map is 10,000 times bigger than reality
Answer: 1 cm on the map = 10,000 cm in real life
A scale of means 1 unit on the map equals 10,000 units in real life. The map is a reduction of reality.
2.
A map has a scale of . A road is 5 cm on the map. How many cm is it in real life?
Answer: 500
. The road is 500 cm (5 meters) in real life.
3.
To create a scale drawing of your room, you need to make it smaller. Should you multiply or divide the actual measurements?
1. a)Multiply by the scale factor
2. b)Add the scale factor
3. c)Divide by the scale factor
4. d)Subtract the scale factor
Answer: Divide by the scale factor
When going from reality to drawing, divide by the scale factor. For example, a 400 cm wall at scale becomes cm.
4.
A room is 800 cm long. You want to draw it at scale . How many cm long will the drawing be?
Answer: 20
. The drawing will be 20 cm long.
5.
On a map with scale , two towns are 8 cm apart. What is the actual distance in kilometers?
Answer: 2
1. What is the scale factor? 25000
2. What is ? (This gives the answer in cm) 200000
3. Convert 200,000 cm to meters (divide by 100) 2000
4. Convert 2,000 m to km (divide by 1,000) 2
6.
A model car is 15 cm long. The real car is 450 cm long. What is the scale of the model?
1. a)
2. b)
3. c)
4. d)
Answer:
Scale = Model : Real = . The model is 1/30 of the real car.
7.
On a blueprint at scale , a window is 2.4 cm wide. What is the actual width in cm?
Answer: 120
. The window is 120 cm (1.2 m) wide in reality.
8.
A bedroom is 5 m by 4 m. You want to draw it at scale . What will the dimensions be in cm?
Answer: 20 by 16
1. Convert 5 m to cm 500
2. Divide 500 cm by 25 for the first dimension 20
3. Convert 4 m to cm 400
4. Divide 400 cm by 25 for the second dimension 16
9.
A floor plan has scale . A couch measures 2 cm on the plan. How long is the actual couch?
1. a)200 cm (2 m)
2. b)2,000 cm (20 m)
3. c)0.02 cm
4. d)20 cm
Answer: 200 cm (2 m)
. A standard couch length!
10.
A model building is 45 cm tall. The actual building is 90 m tall. What scale was used?
Answer: 1:200
1. Convert 90 m to cm 9000
2. Divide the real height by the model height: 200
3. Write the scale as ? 200
11.
On a map with scale , how many cm on the map represents 3.5 km in reality?
Answer: 7
. Map distance = .
12.
An architect's blueprint uses scale . A corridor measures 4 cm on the blueprint. How long is the actual corridor?
1. a)30 cm
2. b)3 m
3. c)3.75 m
4. d)300 cm
Answer: 3 m
. Note: 3 m and 300 cm are the same, but 3 m is the most useful answer.
13.
A park is drawn at scale . The drawing measures 8 cm by 5 cm. What is the actual area of the park in square meters?
Answer: 16000
1. Find the actual length: cm 16000
2. Convert 16,000 cm to m 160
3. Find the actual width: cm 10000
4. Convert 10,000 cm to m 100
5. Calculate area: square meters 16000
14.
A toy train is built at scale . The real train is 174 cm tall. How many cm tall is the toy?
Answer: 2
. The toy train is 2 cm tall. (Scale 1:87 is called HO scale, popular for model railways!)
15.
You want to fit a floor plan of a 12 m by 9 m room on an A4 paper (21 cm by 29.7 cm). What is the largest scale you can use? (Choose from , , or )
Answer: 1:50
1. At scale , what would 12 m (1200 cm) become? 24
2. At scale , what would 9 m (900 cm) become? 18
3. Does 24 cm fit in 29.7 cm? (yes/no) yes
4. Does 18 cm fit in 21 cm? (yes/no) yes