An architect builds a 1/50 scale model of a proposed buildings for a client. The volume of the model is what fraction of the volume of the proposed building?

Question

Mathematics

Alicia Dean

11 December, 03:15

An architect builds a 1/50 scale model of a proposed buildings for a client. The volume of the model is what fraction of the volume of the proposed building?

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Shepherd · Answer 1

Answer: 1/125,000

Step-by-step explanation:

If the lenght of the building is L, the height is H, and the width is W, the volume of the building is V = L*H*W

Then for the model we will have that each measure is 1/50 times the original, this is:

lenght = L/50

height = H/50

widht = W/50

The volume of the scale model is:

V' = (L/50) * (H/50) * (W/50) = L*H*W/50^3

So we have the volume of the actual building divided 50^3

This means that the volume of the scale is 1/50^3 = 1/125,000 times the volume of the actual building.