Scale model

Problem

A $1:50$ scale model of a car is $8$ cm long.

• How long is the real car?
• If the model has a surface area of $96$ cm$^2$, what is the real surface area?
• If the model has a volume of $48$ cm$^3$, what is the real volume?

Solution

The similarity ratio between the real car and the model is $k = 50$. Lengths scale with $k$, areas with $k^2$, volumes with $k^3$.

• Length: $8\times 50 = \boxed{400}$ cm $= 4$ m.
• Surface area: $96\times 50^2 = \boxed{240\,000}$ cm$^2$ $= 24$ m$^2$.
• Volume: $48\times 50^3 = \boxed{6\,000\,000}$ cm$^3$ $= 6$ m$^3$.

Links

Topics: Similarity
Concepts: Scaling laws · Similarity ratio
Methods: Similarity criteria · Homothety transformations
Skills: Modelling · Using formulae
Exercise type: Geometric problem