# scale models and area?

• Jun 7th 2010, 01:17 AM
Neverquit
scale models and area?
Hi ...A scale model of a building has a roof area of 32cm^2. The scale factor is 1:250. Whats the actual roof area in square metres?

Thanks..
• Jun 7th 2010, 01:23 AM
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Quote:

Originally Posted by Neverquit
Hi ...A scale model of a building has a roof area of 32cm^2. The scale factor is 1:250. Whats the actual roof area in square metres?

Thanks..

Hi Neverquit,

The important thing to remember is that a model length L represents real length 250L, but a model area A represents real area (250^2)A. This is apparent if we write

$\displaystyle 1=\frac{1\ \text{model cm}}{250\ \text{real cm}}$

and square both sides. (For some reason, during my studies this was emphasized most in chemistry, not so much math or other sciences.)
• Jun 7th 2010, 04:26 AM
Neverquit
models
Hi I am still not sure?
• Jun 7th 2010, 04:49 AM
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Quote:

Originally Posted by Neverquit
Hi I am still not sure?

$\displaystyle 32\ (\text{model cm})^2 = 32\ (\text{model cm})^2 \cdot \left(\frac{250\ \text{real cm}}{1\ \text{model cm}}\right)^2$
$\displaystyle = 32\ (\text{model cm})^2 \cdot \frac{62500\ (\text{real cm})^2}{1\ (\text{model cm})^2} = 2000000\ (\text{real cm})^2 = 200\ (\text{real m})^2$