Percentages and ratio · Ages 13–14

Scales on maps and plans worksheet

Part of: Rates, ratios & proportions

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Percentages and ratio · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A map's scale is 1 : 200000: 2.5 cm on it stand for km
Answer:
2.A map's scale is 1 : 100000. A real 17 km = cm, which is cm on the map.
Fill in each blank
Answer:
3.A map's scale is 1 : 25000: 7 cm on it stand for km
Answer:
4.11 cm on a map stand for a real 4.4 km. The map's scale is 1 :
Answer:
5.On a map with scale 1 : 1000, a park covers 1 cm². What is the park's real area in m²?
Answer:
6.A map's scale is 1 : 25000. A rectangular plot is 11 cm by 8 cm on it. What is its real area in km²?
Answer:
7.A map's scale is 1 : 100000. A rectangular plot is 8 cm by 3 cm on it. What is its real area in km²?
Answer:

8.On a map with scale 1 : 2000, 1 cm² stands for 400 m².
True or false?
Answer:
9.On a plan with scale 1 : 2000, what real length in metres do 7 cm stand for?
- A. 1400 m
- B. 14000 m
- C. 14 m
- D. 140 m
Choose the right answer
Answer:
10.On a map with scale 1 : 10000, 1 cm² stands for 100 m².
True or false?
Answer:
11.On a plan with scale 1 : 1000, what real length in metres do 3 cm stand for?
- A. 3 m
- B. 3000 m
- C. 30 m
- D. 300 m
Choose the right answer
Answer:
12.The same area of land is drawn on a map with scale 1 : 50000, then on one with scale 1 : 5000. How many times its area on the first map is its area on the second?
- A. 10 times
- B. 0.01 times
- C. 20 times
- D. 100 times
Choose the right answer
Answer:

13.A model of a building is made to a scale of 1 : 20. The model is 27 cm tall. How tall is the real building in metres?
Working:
Answer:
14.A park's real area is 575 m². What is its area in cm² on a map with scale 1 : 500?
Working:
Answer:
15.A map's scale is 1 : 50000. Two stations are 2 cm apart on it: really m, that is km.
Fill in each blank
Working:
Answer:
16.Map A's scale is 1 : 5000 and map B's is 1 : 20000. How many times its area on map B is a lake's area on map A?
- A. 0.25 times
- B. 0.0625 times
- C. 16 times
- D. 4 times
Choose the right answer
Working:
Answer:
17.A floor plan's scale is 1 : 200. A rectangular room on it is 7.5 cm by 3 cm. Flooring costs $110 a m². How much does flooring the whole room cost?
Working:
Answer:
18.On a 1 : 50000 map, two places are 9 cm apart. Find the real distance in km: put the steps in order.
- A. 4500 ÷ 1000 = 4.5
- B. 9 × 50000 = 450000
- C. 450000 ÷ 100 = 4500
Write the letters in the right order
Working:
Answer:

Show the answers and working

Scales on maps and plans worksheet: Answers and working

1. 5
2.5 × 200000 = 500000 cm; 1 km = 100000 cm, so it is 5 km.
2. 1700000, 17
The same unit first: 17 km = 1700000 cm; on the map, 1700000 ÷ 100000 = 17 cm.
3. 1.75
7 × 25000 = 175000 cm; 1 km = 100000 cm, so it is 1.75 km.
4. 40000
In one unit: 4.4 km = 4.4 × 100000 cm, so the scale is 11 : 4.4 × 100000 = 1 : 40000.
5. 100 m²
1 cm stands for 10 m, so 1 cm² for 10 × 10 m²: 1 × 10 × 10 = 100 m².
6. 5.5 km²
1 cm stands for 0.25 km: really 2.75 km by 2 km, an area of 2.75 × 2 = 5.5 km².
7. 24 km²
1 cm stands for 1 km: really 8 km by 3 km, an area of 8 × 3 = 24 km².

8. True
1 cm stands for 20 m, so 1 cm² is 20 m × 20 m = 400 m²: an area takes the scale squared.
9. D. 140 m
Real length = 7 × 2000 = 14000 cm = 140 m.
10. False
1 cm stands for 100 m, so 1 cm² is 100 m × 100 m = 10000 m²: an area takes the scale squared.
11. C. 30 m
Real length = 3 × 1000 = 3000 cm = 30 m.
12. D. 100 times
50000 ÷ 5000 = 10: lengths on the second map are 10 times those on the first, so areas are 10² = 100 times.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 5.4 m
Real height = 27 × 20 cm = 5.4 m.
14. 23 cm²
1 cm stands for 5 m, so 1 cm² for 5 × 5 m²: 575 ÷ (5 × 5) = 23 cm².
15. 1000, 1
2 × 50000 cm ÷ 100 = 1000 m, and 1000 ÷ 1000 = 1 km.
16. C. 16 times
20000 ÷ 5000 = 4: lengths on A are 4 times those on B, so areas are 4 × 4 = 16 times.
17. 9900 dollars
Really 7.5 × 200 cm = 15 m by 6 m, an area of 90 m², costing 90 × 110 = 9900 dollars.
18. B → C → A
Times the scale for cm, then into m, then into km.

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