Let’s solve each problem one by one. We’ll use the scale factor to find missing dimensions. Remember:
Scale factor = model dimension : actual dimension
We can set up a proportion and solve for the missing value.
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Problem 1
Scale:
5 cm = ___ m → This means 5 cm on model = ? meters in real life.
But wait — we’re given:
Model: 9.5 cm
Actual: 30.5 m
So, if 9.5 cm (model) corresponds to 30.5 m (actual), then what does 5 cm correspond to?
Set up proportion:
5 cm / x m = 9.5 cm / 30.5 m
Cross multiply:
5 * 30.5 = 9.5 * x
152.5 = 9.5x
x = 152.5 ÷ 9.5 ≈
16.0526... → Round to nearest tenth →
16.1
✔ Answer for #1:
16.1
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Problem 2
Scale:
2 m = 4 mi
Map: 12 m
Actual: ? mi
Proportion:
2 m / 4 mi = 12 m / x mi
Cross multiply:
2x = 48
x = 24
✔ Answer for #2:
24
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Problem 3
Scale:
2 ft = 10.4 mi
Map: ? ft
Actual: 20.8 mi
Proportion:
2 ft / 10.4 mi = x ft / 20.8 mi
Cross multiply:
10.4x = 2 * 20.8 = 41.6
x = 41.6 ÷ 10.4 =
4
✔ Answer for #3:
4
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Problem 4
Scale:
7 cm = ___ m
Model: 40.4 cm
Actual: 80.6 m
Find what 7 cm represents.
Proportion:
7 cm / x m = 40.4 cm / 80.6 m
Cross multiply:
7 * 80.6 = 40.4 * x
564.2 = 40.4x
x = 564.2 ÷ 40.4 ≈
13.965... → Round to nearest tenth →
14.0
✔ Answer for #4:
14.0
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Problem 5
Scale:
5 m = 15 mi
Map: 7.8 m
Actual: ? mi
Proportion:
5 m / 15 mi = 7.8 m / x mi
Cross multiply:
5x = 15 * 7.8 = 117
x = 117 ÷ 5 =
23.4
✔ Answer for #5:
23.4
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Problem 6
Scale:
6 km = 4 mi
Map: ? km
Actual: 40.1 mi
Proportion:
6 km / 4 mi = x km / 40.1 mi
Cross multiply:
4x = 6 * 40.1 = 240.6
x = 240.6 ÷ 4 =
60.15 → Round to nearest tenth →
60.2
✔ Answer for #6:
60.2
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Problem 7
Scale:
5 cm = ___ m
Model: 40.2 cm
Actual: 60.2 m
Proportion:
5 cm / x m = 40.2 cm / 60.2 m
Cross multiply:
5 * 60.2 = 40.2 * x
301 = 40.2x
x = 301 ÷ 40.2 ≈
7.487... → Round to nearest tenth →
7.5
✔ Answer for #7:
7.5
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Problem 8
Scale:
4 m = 18 mi
Map: 6.8 m
Actual: ? mi
Proportion:
4 m / 18 mi = 6.8 m / x mi
Cross multiply:
4x = 18 * 6.8 = 122.4
x = 122.4 ÷ 4 =
30.6
✔ Answer for #8:
30.6
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Problem 9
Scale:
4 ft = 16 mi
Map: ? ft
Actual: 80 mi
Proportion:
4 ft / 16 mi = x ft / 80 mi
Cross multiply:
16x = 4 * 80 = 320
x = 320 ÷ 16 =
20
✔ Answer for #9:
20
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Problem 10
Scale:
8 cm = ___ m
Model: 80.8 cm
Actual: 90.6 m
Proportion:
8 cm / x m = 80.8 cm / 90.6 m
Cross multiply:
8 * 90.6 = 80.8 * x
724.8 = 80.8x
x = 724.8 ÷ 80.8 ≈
8.970... → Round to nearest tenth →
9.0
✔ Answer for #10:
9.0
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Final Answer:
1. 16.1
2. 24
3. 4
4. 14.0
5. 23.4
6. 60.2
7. 7.5
8. 30.6
9. 20
10. 9.0
Parent Tip: Review the logic above to help your child master the concept of geometry scale factor worksheet.
