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Math help? One question?
1. The scale factor of a model of a swimming pool is 1 to 20. The volume of the actual pool is 400m3.
What is the volume of the model?
A) 20 m3
B) 1 m3
C) 0.15 m3
D) 0.05 m3
1 Answer
- PuzzlingLv 75 years ago
In general:
The scale of the two objects is a:b.
The ratio of their areas would be a²:b²
The ratio of their volumes would be a^3:b^3
In your case, the scale is 1:20, so the ratio of the volumes is 1^3:20^3 = 1:8000
Set up a proportion:
x/400 = 1/8000
Multiply both sides by 400:
x = 400/8000
x = 1/20 (or 0.05)
Answer:
D) 0.05 m^3
If this isn't clear, just make up some dimensions for the pool. For example, the pool could be: 10m by 20m and 2m deep:
10 x 20 x 2 = 400 m^3
Now scale those down to the model size by dividing each by 20:
1/2m x 1m * 1/10m
= 1/20 m^3
Answer:
D. 0.05 m^3
