Question

An architect creates a scale model. The volume of the scale model is 0.1 cubic meters. The volume of the real-world

building is 100,000 cubic meters. What is the ratio of corresponding sides from model to real world?

Answer 1

1:0.4641

Explanation:

We are told that the scale of the model with respect to the real world is 0.1 cubic meter. This means that for every 1 cubic meter in the real world the model represents 0.1.

They tell us that the real world volume is 100,000, that if we assume a cube, we have to:

V = l ^ 3

l = 100000 ^ (1/3)

l = 46.41

46.41 meters would be each side, now the volume of the model would be:

100,000 * 0.1 = 10,000

Which means that its sides would be:

V = l ^ 3

l = 100000 ^ (1/3)

l = 21.54

We calculate the scale of the sides:

21.54 / 46.41 = 0.4641

Which means that for every 1 meter in the real world the model represents 0.4641 meters.